PROGRAM ANCONT C -------------- C C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C CODE ANCONT 1.00 C C TO EVALUATE THE MELLIN TRANSFORMS OF NIELSEN INTEGRALS AND RELATED C FUNCTIONS AND THEIR ANALYTIC CONTINUATIONS INTO THE COMPLEX PLANE C FOR ALL HARMONIC SUMS OCCURING UP TO THE 2--LOOP LEVEL C (TRANSCENDENTALITY 4) C C************************************************************************ C C REFS.: [1] J. BLUEMLEIN AND S. KURTH, DESY 97-160, HEP-PH/9708388 C [2] J. BLUEMLEIN AND S. KURTH, PHYS. REV. D60 (1999) 014018 C [3] J. BLUEMLEIN Comput. Phys. Commun. 133 (2000) 76. C C >>> Conditions of use: Citation of Refs.: [2] and [3] C >>> Compilation g77 ancont.f C C************************************************************************ C C IMPLICIT REAL*8 (A-H,O-Z) C C-------------- START C CALL ACSTAR C C C-------------- INITIALIZATION C CALL ACINI C C-------------- RUNNING C CALL ACRUN C C-------------- END C CALL ACEND C STOP END SUBROUTINE ACSTAR C ----------------- C WRITE(6,*) ' ' WRITE(6,*) '***** ANCONT: VS 1.00 *****' WRITE(6,*) '***** J. BLUEMLEIN 01.10.1999 *****' WRITE(6,*) ' ' WRITE(6,*) ' ' C RETURN END SUBROUTINE ACINI C ---------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- INITIALIZE CONSTANTS C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /KM/KEY,MAX C COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/ACCON5/ XLI4 COMMON/IAPP / IAPP COMMON/VAL / ZERO,ONE COMMON/ACLOG1/ AK1(9) COMMON/ACLOG2/ AK2(10) COMMON/ACLOG3/ AK3(11) COMMON/ACLOG4/ BK1(9) COMMON/ACLOG5/ BK2(10) COMMON/ACLOG6/ CK1(12) COMMON/ACLOG7/ CK2(13) COMMON/ACLOG8/ CK3(10) COMMON/ACLOG9/ CK4(13) COMMON/ACLG10/ CK5(9) COMMON/ACLG11/ DK5(10) COMMON/POLY1 / P21(4) COMMON/POLY2 / P22(4) COMMON/POLY3 / P23(5),P33(5) COMMON/POLY4 / P24(5),P34(5) C DIMENSION P11(4),P12(4),P13(5),P14(5) C DATA AK1/0.999999974532240D+0, & -0.499995525890027D+0, & 0.333203435554182D+0, & -0.248529457735332D+0, & 0.191451164493502D+0, & -0.137466222203386D+0, & 0.792107405737825D-1, & -0.301109652783781D-1, & 0.538406198111749D-2/ C DATA AK2/0.999999980543793D+0, & -0.999995797779624D+0, & 0.916516447393493D+0, & -0.831229921350708D+0, & 0.745873737923571D+0, & -0.634523908078600D+0, & 0.467104011423750D+0, & -0.261348046799178D+0, & 0.936814286867420D-1, & -0.156249375012462D-1/ C DATA AK3/9.99999989322696D-1, & -1.49999722020708D+0, & 1.74988008499745D+0, & -1.87296689068405D+0, & 1.91539974617231D+0, & -1.85963744001295D+0, & 1.62987195424434D+0, & -1.17982353224299D+0, & 6.28710122994999D-1, & -2.11307487211713D-1, & 3.28953352932140D-2/ C DATA BK1/0.693147166991375D+0, & -0.306850436868254D+0, & 0.193078041088284D+0, & -0.139403892894644D+0, & 0.105269615988049D+0, & -0.746801353858524D-1, & 0.427339135378207D-1, & -0.161809049989783D-1, & 0.288664611077007D-2/ C DATA BK2/0.480453024731510D+0, & 0.480450679641120D+0, & -0.519463586324817D+0, & 0.479285947990175D+0, & -0.427765744446172D+0, & 0.360855321373065D+0, & -0.263827078164263D+0, & 0.146927719341510D+0, & -0.525105367350968D-1, & 0.874144396622167D-2/ C DATA CK1/-0.283822933724932D+0, & 0.999994319023731D+0, & -0.124975762907682D+1, & 0.607076808008983D+0, & -0.280403220046588D-1, & -0.181869786537805D+0, & 0.532318519269331D+0, & -0.107281686995035D+1, & 0.138194913357518D+1, & -0.111100841298484D+1, & 0.506649587198046D+0, & -0.100672390783659D+0/ C DATA CK2/ 0.480322239287449D+0, & -0.168480825099580D+1, & 0.209270571620726D+1, & -0.101728150275998D+1, & 0.160179976133047D+0, & -0.351982236677917D+0, & 0.141033316846244D+1, & -0.353343997843391D+1, & 0.593934696819832D+1, & -0.660019784804042D+1, & 0.466330349413063D+1, & -0.189825467489058D+1, & 0.339772909487512D+0/ C DATA CK3/-0.243948949064443D-1, & 0.000005136294145D+0, & 0.249849075518710D+0, & -0.498290708990997D+0, & 0.354866791547134D+0, & -0.522116678353452D-1, & -0.648354706049337D-1, & 0.644165053822532D-1, & -0.394927322542075D-1, & 0.100879370657869D-1/ C DATA CK4/ 0.192962504274437D+0, & 0.000005641557253D+0, & -0.196891075399448D+1, & 0.392919138747074D+1, & -0.290306105685546D+1, & 0.992890266001707D+0, & -0.130026190226546D+1, & 0.341870577921103D+1, & -0.576763902370864D+1, & 0.645554138192407D+1, & -0.459405622046138D+1, & 0.188510809558304D+1, & -0.340476080290674D+0/ C DATA CK5/-0.822467033400775D+0, & 0.887664705657325D-1, & -0.241549406045162D-1, & 0.965074750946139D-2, & -0.470587487919749D-2, & 0.246014308378549D-2, & -0.116431121874067D-2, & 0.395705193848026D-3, & -0.664699010014505D-4/ C DATA DK5/-0.822467033400775D+0, & 0.999999974532240D+0, & -0.249997762945014D+0, & 0.111067811851394D+0, & -0.621323644338330D-1, & 0.382902328987004D-1, & -0.229110370338977D-1, & 0.113158200819689D-1, & -0.376387065979726D-2, & 0.598229109013054D-3/ C PI = 3.141592653589793238462643D0 ZETA2 = PI**2/6.0D0 ZETA3 = 1.20205690315959428540D0 ZET2=ZETA2 ZET3=ZETA3 ZLI4 = FLI4(0.5D0) XLI4 = FLI4(0.5D0) D2 = DLOG(2.0D0) DL = DLOG(2.0D0) GE = 0.57721566490153D+0 C ZERO=0.0D0 ONE =1.0D0 C C---------------------------------------------------------------------- P11(1)=-49.0D0/36.0+ZETA2 P11(2)=11.0D0/6.0D0 P11(3)=-7.0D0/12.0D0 P11(4)=1.0D0/9.0D0 C------------------------------- P21(1)=11.0D0/6.0 P21(2)=-3.0D0 P21(3)=3.0D0/2.0D0 P21(4)=-1.0D0/3.0D0 C------------------------------- P12(1)=ZETA3-11.0D0/6.0*ZETA2+4.0D0/3.0D0 P12(2)=3.0D0*ZETA2-13.0D0/4.0D0 P12(3)=-3.0D0/2.0D0*ZETA2+5.0D0/2.0D0 P12(4)=1.0D0/3.0D0*ZETA2-7.0D0/12.0D0 C------------------------------- P22(1)=-1.0D0 P22(2)=5.0D0/2.0D0 P22(3)=-2.0D0 P22(4)=1.0D0/2.0D0 C------------------------------- P13(1)=ZETA3-2035.0D0/1728.0D0 P13(2)=205.0D0/144.0D0 P13(3)=-95.0D0/288.0D0 P13(4)=43.0D0/432.0D0 P13(5)=-1.0D0/64.0D0 C------------------------------- P23(1)=205.0D0/144.0D0 P23(2)=-25.0D0/12.0D0 P23(3)=23.0D0/24.0D0 P23(4)=-13.0D0/36.0D0 P23(5)=1.0D0/16.0D0 C------------------------------- P33(1)=-25.0D0/24.0D0 P33(2)=2.0D0 P33(3)=-3.0D0/2.0D0 P33(4)=2.0D0/3.0D0 P33(5)=-1.0D0/8.0D0 C------------------------------- P14(1)=257.D0/144.0D0-205.0D0/72.0D0*ZET2+ZET2**2 P14(2)=-167.0D0/36.0D0+25.0D0/6.0D0*ZET2 P14(3)=101.0D0/24.0D0-23.0D0/12.0D0*ZET2 P14(4)=-59.0D0/36.0D0+13.0D0/18.0D0*ZET2 P14(5)=41.0D0/144.0D0-ZET2/8.0D0 C------------------------------- P24(1)=-167.0D0/36.0D0+25.0D0/6.0D0*ZET2 P24(2)=235.0D0/18.0D0-8.0D0*ZET2 P24(3)=-40.0D0/3.0D0+6.0D0*ZET2 P24(4)=109.0D0/18.0D0-8.0D0/3.0D0*ZET2 P24(5)=-41.0D0/36.0D0+ZET2/2.0D0 C------------------------------- P34(1)=35.0D0/12.0D0 P34(2)=-26.0D0/3.0D0 P34(3)=19.0D0/2.0D0 P34(4)=-14.0D0/3.0D0 P34(5)=11.0D0/12.0D0 C---------------------------------------------------------------------- C C >>> ACCOUNT FOR POLYNOM PARTS C CK1(1)=CK1(1)+P11(1) CK1(2)=CK1(2)+P11(2) CK1(3)=CK1(3)+P11(3) CK1(4)=CK1(4)+P11(4) C CK2(1)=CK2(1)+P12(1) CK2(2)=CK2(2)+P12(2) CK2(3)=CK2(3)+P12(3) CK2(4)=CK2(4)+P12(4) C CK3(1)=CK3(1)+P13(1) CK3(2)=CK3(2)+P13(2) CK3(3)=CK3(3)+P13(3) CK3(4)=CK3(4)+P13(4) CK3(5)=CK3(5)+P13(5) C CK4(1)=CK4(1)+P14(1) CK4(2)=CK4(2)+P14(2) CK4(3)=CK4(3)+P14(3) CK4(4)=CK4(4)+P14(4) CK4(5)=CK4(5)+P14(5) C C---------------------------------------------------------------------- C KEY = 2 MAX = 10000 C IAPP=1 C CALL INVINI C CALL DEFAUL C CALL UINIT C CALL WROUT C RETURN END SUBROUTINE INVINI C ----------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- INITIALIZE CONSTANTS: MELLIN INVERSION C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) * COMMON /OFFS / CP(26) COMMON /PI / PI COMMON /ZET2/ ZETA2 COMMON /ZET3/ ZETA3 COMMON /WGAUSS/ XL8(8),WL8(8),XL32(32),WL32(32) * DATA PI/ 3.14159265358979323846D+0/ * 1 2 3 4 5 6 7 DATA CP/-0.7D0,-1.7D0,-0.8D0,-0.7D0,-0.7D0,-0.7D0,-0.7D0, & -1.7D0,-1.7D0,-1.7D0,-1.7D0,-1.7D0,-1.7D0, 0.3D0, & -0.7D0,-0.7D0,-1.7D0, 0.3D0, 0.3D0, 0.3D0, 0.2D0, & -0.5D0, 0.5D0, 0.5D0,0.5D0,-2.8D0/ * DATA XL8/-0.960289856497536231684D+0, & -0.796666477413626739592D+0, & -0.525532409916328985818D+0, & -0.183434642495649804939D+0, & 0.183434642495649804939D+0, & 0.525532409916328985818D+0, & 0.796666477413626739592D+0, & 0.960289856497536231684D+0/ * DATA WL8/ 0.101228536290376259163D+0, & 0.222381034453374470518D+0, & 0.313706645877887287348D+0, & 0.362683783378361982964D+0, & 0.362683783378361982964D+0, & 0.313706645877887287348D+0, & 0.222381034453374470518D+0, & 0.101228536290376259163D+0/ * DATA XL32/-0.997263861849481563545D+0, & -0.985611511545268335400D+0, & -0.964762255587506430774D+0, & -0.934906075937739689171D+0, & -0.896321155766052123965D+0, & -0.849367613732569970134D+0, & -0.794483795967942406963D+0, & -0.732182118740289680387D+0, & -0.663044266930215200975D+0, & -0.587715757240762329041D+0, & -0.506899908932229390024D+0, & -0.421351276130635345364D+0, & -0.331868602282127649780D+0, & -0.239287362252137074545D+0, & -0.144471961582796493485D+0, & -0.483076656877383162348D-1, & 0.483076656877383162348D-1, & 0.144471961582796493485D+0, & 0.239287362252137074545D+0, & 0.331868602282127649780D+0, & 0.421351276130635345364D+0, & 0.506899908932229390024D+0, & 0.587715757240762329041D+0, & 0.663044266930215200975D+0, & 0.732182118740289680387D+0, & 0.794483795967942406963D+0, & 0.849367613732569970134D+0, & 0.896321155766052123965D+0, & 0.934906075937739689171D+0, & 0.964762255587506430774D+0, & 0.985611511545268335400D+0, & 0.997263861849481563545D+0/ * DATA WL32/0.701861000943074980416D-2, & 0.162743947308230037851D-1, & 0.253920653084367920322D-1, & 0.342738629139351946052D-1, & 0.428358980239763007216D-1, & 0.509980592613025930634D-1, & 0.586840934788972562042D-1, & 0.658222227761892440852D-1, & 0.723457941088502071174D-1, & 0.781938957870682705896D-1, & 0.833119242269464135758D-1, & 0.876520930044038163114D-1, & 0.911738786957638874594D-1, & 0.938443990808045654352D-1, & 0.956387200792748594152D-1, & 0.965400885147278005676D-1, & 0.965400885147278005676D-1, & 0.956387200792748594152D-1, & 0.938443990808045654352D-1, & 0.911738786957638874594D-1, & 0.876520930044038163114D-1, & 0.833119242269464135758D-1, & 0.781938957870682705896D-1, & 0.723457941088502071174D-1, & 0.658222227761892440852D-1, & 0.586840934788972562042D-1, & 0.509980592613025930634D-1, & 0.428358980239763007216D-1, & 0.342738629139351946052D-1, & 0.253920653084367920322D-1, & 0.162743947308230037851D-1, & 0.701861000943074980416D-2/ * ZETA2=PI**2/6.0D0 ZETA3=1.20205690315959428540D+0 * PHI=3.0D0/4.0D0*PI PHI=9.0D0/10.0D0*PI * RETURN END SUBROUTINE DEFAUL C ----------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- DEFAULT PARAMETERS C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /EP/EPS COMMON/RUN / IRUN COMMON/TEST/ ITEST1,ITEST2,ITEST3 COMMON/MOMPA/ NMIN,NMAX COMMON/FUNPA/ IMIN,IMAX COMMON/IAPP / IAPP C EPS = 1.0D-9 IRUN = 1 ITEST1=1 ITEST2=1 ITEST3=1 IMIN=1 IMAX=26 NMIN=1 NMAX=20 IAPP=1 C RETURN END SUBROUTINE WROUT C ---------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- WRITE OUT OF THE DEFAULT PARAMETERS C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /EP/EPS COMMON/TEST/ ITEST1,ITEST2,ITEST3 COMMON/MOMPA/ NMIN,NMAX COMMON/FUNPA/ IMIN,IMAX COMMON/IAPP / IAPP COMMON/RUN / IRUN C WRITE(6,*) ' ' WRITE(6,*) '*** INPUT PARAMETERS :' WRITE(6,*) ' ' WRITE(6,*) '*** IRUN = ', IRUN WRITE(6,*) '*** ITEST1 = ', ITEST1 WRITE(6,*) '*** ITEST2 = ', ITEST2 WRITE(6,*) '*** ITEST3 = ', ITEST3 WRITE(6,*) '*** IMIN = ', IMIN WRITE(6,*) '*** IMAX = ', IMAX WRITE(6,*) '*** NMIN = ', NMIN WRITE(6,*) '*** NMAX = ', NMAX WRITE(6,*) '*** IAPP = ', IAPP WRITE(6,*) '*** EPS = ', EPS WRITE(6,*) ' ' WRITE(6,*) ' ' C RETURN END SUBROUTINE ACRUN C ---------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- RUNNING THE CODE C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMPLEX*16 ACG1,ACG2,ACG3,ACG4,ACG5,ACG6,ACG7,ACG8,ACG9,ACG10, & ACG11,ACG12,ACG13,ACG14,ACG15,ACG16,ACG17,ACG18,ACG19, & ACG20,ACG21,ACG22,ACG23,ACG24,ACG25,ACG26,ZZ,R C COMMON/TEST/ ITEST1,ITEST2,ITEST3 COMMON/MOMPA/ NMIN,NMAX COMMON/FUNPA/ IMIN,IMAX COMMON/IAPP / IAPP COMMON/RUN / IRUN C DIMENSION XP(26) C DATA XP/1.0D-7,1.0D-6,1.0D-5,1.0D-4,1.0D-3,1.0D-2,5.0D-2, & 1.0D-1,1.5D-1,2.0D-1,2.5D-1,3.0D-1,3.5D-1,4.0D-1, & 4.5D-1,5.0D-1,5.5D-1,6.0D-1,6.5D-1,7.0D-1,7.5D-1, & 8.0D-1,8.5D-1,9.0D-1,9.5D-1,9.9D-1/ C C--- RUNNING THE CODE C I1=0 I2=0 I3=0 IF(IRUN.LT.0.OR.IRUN.GT.5) GOTO 3000 IF(IRUN.EQ.0.AND.ITEST1.EQ.1) I1=1 IF(IRUN.EQ.0.AND.ITEST2.EQ.1) I2=1 IF(IRUN.EQ.0.AND.ITEST3.EQ.1) I3=1 IF(I1.NE.1.AND.I2.NE.1.AND.I3.NE.1) GOTO 3001 GOTO 3002 3000 WRITE(6,*) '***** IRUN=',IRUN,' ** OUT OF RANGE, STOP ***' STOP 3002 CONTINUE IF(ITEST1.EQ.1) GOTO 101 1001 IF(ITEST2.EQ.1) GOTO 102 1002 IF(ITEST3.EQ.1) GOTO 103 GOTO 1000 C C--- TEST 1: POSITIVE INTEGER MOMENTS: NUM. REPRESENTATION VS HARMONIC C SUMS C 101 CONTINUE C DO 1 I=IMIN,IMAX WRITE(6,*) '****************************************' DO 2 N=NMIN,NMAX C CALL MOMTES(I,N,RES,F1) C WRITE(6,2003) I,N,RES,F1 2003 FORMAT(1X,'TEST1: I,K,R=',I4,1X,I4,1X,E12.3,1X,E12.5) C 2 CONTINUE WRITE(6,*) '****************************************' 1 CONTINUE C GOTO 1001 C 102 CONTINUE C C--- TEST 2: POSITIVE INTEGER MOMENTS: HARMONIC SUMS VS COMPLEX MOMENT C REPRESENTATION C DO 3 I=IMIN,IMAX WRITE(6,*) '****************************************' DO 4 N=NMIN,NMAX C CALL ACREL(I,N,RES) C IF(I.NE.3) THEN WRITE(6,2001) I,N,RES 2001 FORMAT(1X,'TEST2: I,N,R=',I4,1X,I4,1X,E12.3) ELSE WRITE(6,2002) IAPP,I,N,RES 2002 FORMAT(1X,'TEST2: IAPP,I,K,R=',I4,1X,I4,1X,I4,1X,D12.3) ENDIF C 4 CONTINUE WRITE(6,*) '****************************************' 3 CONTINUE C GOTO 1002 C 103 CONTINUE C C--- TEST 3: X DEPENDENCE OF BASIC FUNCTIONS: NUM. RESULTS AGAINST C MELLIN INVERSION C * DO 5 I=IMIN,IMAX WRITE(6,*) &'**********************************************************' WRITE(6,*) ' ' WRITE(6,*) '*** I = ',I,' ***' WRITE(6,*) ' ' DO 6 J=1,26 C X=XP(J) CALL INVERS(X,I,RES,F1) C WRITE(6,9000) X,RES,F1 9000 FORMAT('TEST3:X,RAT,VAL=',D12.5,3X,D12.5,3X,D12.5) C 6 CONTINUE WRITE(6,*) &'**********************************************************' 5 CONTINUE GOTO 1000 3001 CONTINUE C C >>> IRUN=1,2,3,4,5 C GOTO(4001,4002,4003,4004,4005), IRUN C 4001 CONTINUE C DO 5001 II=IMIN,IMAX DO 5002 NN=NMIN,NMAX IF(II.EQ.1) T=FCT1(NN) IF(II.EQ.2) T=FCT2(NN) IF(II.EQ.3) T=FCT3(NN) IF(II.EQ.4) T=FCT4(NN) IF(II.EQ.5) T=FCT5(NN) IF(II.EQ.6) T=FCT6(NN) IF(II.EQ.7) T=FCT7(NN) IF(II.EQ.8) T=FCT8(NN) IF(II.EQ.9) T=FCT9(NN) IF(II.EQ.10) T=FCT10(NN) IF(II.EQ.11) T=FCT11(NN) IF(II.EQ.12) T=FCT12(NN) IF(II.EQ.13) T=FCT13(NN) IF(II.EQ.14) T=FCT14(NN) IF(II.EQ.15) T=FCT15(NN) IF(II.EQ.16) T=FCT16(NN) IF(II.EQ.17) T=FCT17(NN) IF(II.EQ.18) T=FCT18(NN) IF(II.EQ.19) T=FCT19(NN) IF(II.EQ.20) T=FCT20(NN) IF(II.EQ.21) T=FCT21(NN) IF(II.EQ.22) T=FCT22(NN) IF(II.EQ.23) T=FCT23(NN) IF(II.EQ.24) T=FCT24(NN) IF(II.EQ.25) T=FCT25(NN) IF(II.EQ.26) T=FCT26(NN) C WRITE(6,7001) II,NN,T 7001 FORMAT(1X,'IRUN=1 *** I,N, MOM=',I4,1X,I4,1X,E12.5) 5002 CONTINUE 5001 CONTINUE GOTO 1000 4002 CONTINUE C DO 5003 II=IMIN,IMAX DO 5004 NN=NMIN,NMAX IF(II.EQ.1) T=XCG1(NN) IF(II.EQ.2) T=XCG2(NN) IF(II.EQ.3) T=XCG3(NN) IF(II.EQ.4) T=XCG4(NN) IF(II.EQ.5) T=XCG5(NN) IF(II.EQ.6) T=XCG6(NN) IF(II.EQ.7) T=XCG7(NN) IF(II.EQ.8) T=XCG8(NN) IF(II.EQ.9) T=XCG9(NN) IF(II.EQ.10) T=XCG10(NN) IF(II.EQ.11) T=XCG11(NN) IF(II.EQ.12) T=XCG12(NN) IF(II.EQ.13) T=XCG13(NN) IF(II.EQ.14) T=XCG14(NN) IF(II.EQ.15) T=XCG15(NN) IF(II.EQ.16) T=XCG16(NN) IF(II.EQ.17) T=XCG17(NN) IF(II.EQ.18) T=XCG18(NN) IF(II.EQ.19) T=XCG19(NN) IF(II.EQ.20) T=XCG20(NN) IF(II.EQ.21) T=XCG21(NN) IF(II.EQ.22) T=XCG22(NN) IF(II.EQ.23) T=XCG23(NN) IF(II.EQ.24) T=XCG24(NN) IF(II.EQ.25) T=XCG25(NN) IF(II.EQ.26) T=XCG26(NN) C WRITE(6,7002) II,NN,T 7002 FORMAT(1X,'IRUN=2 *** I,N, MOM=',I4,1X,I4,1X,E12.5) 5004 CONTINUE 5003 CONTINUE GOTO 1000 4003 CONTINUE C DO 5005 II=IMIN,IMAX DO 5006 NN=NMIN,NMAX R=DCMPLX(DBLE(NN),0.0D0) IF(II.EQ.1) ZZ=ACG1(R) IF(II.EQ.2) ZZ=ACG2(R) IF(II.EQ.3) ZZ=ACG3(R) IF(II.EQ.4) ZZ=ACG4(R) IF(II.EQ.5) ZZ=ACG5(R) IF(II.EQ.6) ZZ=ACG6(R) IF(II.EQ.7) ZZ=ACG7(R) IF(II.EQ.8) ZZ=ACG8(R) IF(II.EQ.9) ZZ=ACG9(R) IF(II.EQ.10) ZZ=ACG10(R) IF(II.EQ.11) ZZ=ACG11(R) IF(II.EQ.12) ZZ=ACG12(R) IF(II.EQ.13) ZZ=ACG13(R) IF(II.EQ.14) ZZ=ACG14(R) IF(II.EQ.15) ZZ=ACG15(R) IF(II.EQ.16) ZZ=ACG16(R) IF(II.EQ.17) ZZ=ACG17(R) IF(II.EQ.18) ZZ=ACG18(R) IF(II.EQ.19) ZZ=ACG19(R) IF(II.EQ.20) ZZ=ACG20(R) IF(II.EQ.21) ZZ=ACG21(R) IF(II.EQ.22) ZZ=ACG22(R) IF(II.EQ.23) ZZ=ACG23(R) IF(II.EQ.24) ZZ=ACG24(R) IF(II.EQ.25) ZZ=ACG25(R) IF(II.EQ.26) ZZ=ACG26(R) C WRITE(6,*) 'IRUN=3 ***, I,N, MOM=',II,R,ZZ 5006 CONTINUE 5005 CONTINUE GOTO 1000 C 4004 CONTINUE DO 5007 II=IMIN,IMAX DO 5008 IX=1,26 C X=XP(IX) IF(II.EQ.1) T=FKN1(X) IF(II.EQ.2) T=FKN2(X) IF(II.EQ.3) T=FKN3(X) IF(II.EQ.4) T=FKN4(X) IF(II.EQ.5) T=FKN5(X) IF(II.EQ.6) T=FKN6(X) IF(II.EQ.7) T=FKN7(X) IF(II.EQ.8) T=FKN8(X) IF(II.EQ.9) T=FKN9(X) IF(II.EQ.10) T=FKN10(X) IF(II.EQ.11) T=FKN11(X) IF(II.EQ.12) T=FKN12(X) IF(II.EQ.13) T=FKN13(X) IF(II.EQ.14) T=FKN14(X) IF(II.EQ.15) T=FKN15(X) IF(II.EQ.16) T=FKN16(X) IF(II.EQ.17) T=FKN17(X) IF(II.EQ.18) T=FKN18(X) IF(II.EQ.19) T=FKN19(X) IF(II.EQ.20) T=FKN20(X) IF(II.EQ.21) T=FKN21(X) IF(II.EQ.22) T=FKN22(X) IF(II.EQ.23) T=FKN23(X) IF(II.EQ.24) T=FKN24(X) IF(II.EQ.25) T=FKN25(X) IF(II.EQ.26) T=FKN26(X) C WRITE(6,*) II,X,T 7004 FORMAT(1X,'IRUN=4 *** I,X, FUN=',I4,1X,E12.3,1X,E12.5) 5008 CONTINUE 5007 CONTINUE GOTO 1000 C 4005 CONTINUE C DO 5009 II=IMIN,IMAX DO 5010 IX=1,26 C X=XP(IX) CALL INV1(X,II,F2) C WRITE(6,*) II,X,F2 7005 FORMAT(1X,'IRUN=5 *** I,X, FUN=',I4,1X,E12.3,1X,E12.5) 5010 CONTINUE 5009 CONTINUE C 1000 CONTINUE C C CALL URUN C RETURN END SUBROUTINE MOMTES(I,N,RES,F1) C ----------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- CALCULATE THE RELATIVE ACCURACY OF THE Nth MOMENT COMPARING C--- THE REPRESENTATION THROUGH A NUMERICAL INTEGRAL FCTi WITH THAT C--- BY (ALTERNATING) NESTED HARMONIC SUMS XCGi C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON/IAPP / IAPP COMMON/VAL / ZERO,ONE C EXTERNAL FCT1,FCT2,FCT3,FCT4,FCT5,FCT6,FCT7,FCT8,FCT9,FCT10, & FCT11,FCT12,FCT13,FCT14,FCT15,FCT16,FCT17,FCT18,FCT19, & FCT20,FCT21,FCT22,FCT23,FCT24,FCT25,FCT26 EXTERNAL XCG1,XCG2,XCG3,XCG4,XCG5,XCG6,XCG7,XCG8,XCG9,XCG10, & XCG11,XCG12,XCG13,XCG14,XCG15,XCG16,XCG17,XCG18,XCG19, & XCG20,XCG21,XCG22,XCG23,XCG24,XCG25,XCG26 C ZN=DCMPLX(DBLE(N),ZERO) C GOTO(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22, & 23,24,25,26), I C IF(I.LT.1.OR.I.GT.26) &WRITE(6,*) '*** FLAG I WRONG IN SR MOMTES,I=',I,' *** STOP ***' IF(I.LT.1.OR.I.GT.26) STOP C 1 F1=XCG1(N) RES=F1/FCT1(N)-ONE RETURN 2 F1=XCG2(N) RES=F1/FCT2(N)-ONE RETURN 3 F1=XCG3(N) RES=F1/FCT3(N)-ONE RETURN 4 F1=XCG4(N) RES=F1/FCT4(N)-ONE RETURN 5 F1=XCG5(N) RES=F1/FCT5(N)-ONE RETURN 6 F1=XCG6(N) RES=F1/FCT6(N)-ONE RETURN 7 F1=XCG7(N) RES=F1/FCT7(N)-ONE RETURN 8 F1=XCG8(N) RES=F1/FCT8(N)-ONE RETURN 9 F1=XCG9(N) RES=F1/FCT9(N)-ONE RETURN 10 F1=XCG10(N) RES=F1/FCT10(N)-ONE RETURN 11 F1=XCG11(N) RES=F1/FCT11(N)-ONE RETURN 12 F1=XCG12(N) RES=F1/FCT12(N)-ONE RETURN 13 F1=XCG13(N) RES=F1/FCT13(N)-ONE RETURN 14 F1=XCG14(N) RES=F1/FCT14(N)-ONE RETURN 15 F1=XCG15(N) RES=F1/FCT15(N)-ONE RETURN 16 F1=XCG16(N) RES=F1/FCT16(N)-ONE RETURN 17 F1=XCG17(N) RES=F1/FCT17(N)-ONE RETURN 18 F1=XCG18(N) RES=F1/FCT18(N)-ONE RETURN 19 F1=XCG19(N) RES=F1/FCT19(N)-ONE RETURN 20 F1=XCG20(N) RES=F1/FCT20(N)-ONE RETURN 21 F1=XCG21(N) RES=F1/FCT21(N)-ONE RETURN 22 F1=XCG22(N) RES=F1/FCT22(N)-ONE RETURN 23 F1=XCG23(N) RES=F1/FCT23(N)-ONE RETURN 24 F1=XCG24(N) RES=F1/FCT24(N)-ONE RETURN 25 F1=XCG25(N) RES=F1/FCT25(N)-ONE RETURN 26 F1=XCG26(N) RES=F1/FCT26(N)-ONE RETURN END SUBROUTINE ACREL(I,N,RES) C ------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- CALCULATE THE RELATIVE ACCURACY OF THE Nth MOMENT COMPARING C--- THE REPRESENTATION FOR THE COMPLEX MELLIN MOMENTS ACGi C--- WITH THOSE DUE TO FINITE (ALTERNATING) HARMONIC SUMS XCGi C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 ZERO,ONE,XCG1,XCG2,XCG3,XCG4,XCG5,XCG6 REAL*8 XCG7,XCG8,XCG9,XCG10,XCG11,XCG12 REAL*8 XCG13,XCG14,XCG15,XCG16,XCG17,XCG18 REAL*8 XCG19,XCG20,XCG21,XCG22,XCG23,XCG24 REAL*8 XCG25,XCG26 C REAL*8 RES INTEGER I,IAPP COMMON/IAPP / IAPP COMMON/VAL / ZERO,ONE C EXTERNAL ACG1,ACG2,ACG3,ACG4,ACG5,ACG6,ACG7,ACG8,ACG9,ACG10, & ACG11,ACG12,ACG13,ACG14,ACG15,ACG16,ACG17,ACG18,ACG19, & ACG20,ACG21,ACG22,ACG23,ACG24,ACG25,ACG26 EXTERNAL XCG1,XCG2,XCG3,XCG4,XCG5,XCG6,XCG7,XCG8,XCG9,XCG10, & XCG11,XCG12,XCG13,XCG14,XCG15,XCG16,XCG17,XCG18,XCG19, & XCG20,XCG21,XCG22,XCG23,XCG24,XCG25,XCG26 C ZN=DCMPLX(DBLE(N),ZERO) C GOTO(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22, & 23,24,25,26), I C IF(I.LT.1.OR.I.GT.26) &WRITE(6,*) '*** FLAG I WRONG IN SR ACREL, I=',I,' *** STOP ***' IF(I.LT.1.OR.I.GT.26) STOP C 1 RES=DREAL(ACG1(ZN)/XCG1(N))-ONE RETURN 2 RES=DREAL(ACG2(ZN)/XCG2(N))-ONE RETURN 3 RES=DREAL(ACG3(ZN)/XCG3(N))-ONE RETURN 4 RES=DREAL(ACG4(ZN)/XCG4(N))-ONE RETURN 5 RES=DREAL(ACG5(ZN)/XCG5(N))-ONE RETURN 6 RES=DREAL(ACG6(ZN)/XCG6(N))-ONE RETURN 7 RES=DREAL(ACG7(ZN)/XCG7(N))-ONE RETURN 8 RES=DREAL(ACG8(ZN)/XCG8(N))-ONE RETURN 9 RES=DREAL(ACG9(ZN)/XCG9(N))-ONE RETURN 10 RES=DREAL(ACG10(ZN)/XCG10(N))-ONE RETURN 11 RES=DREAL(ACG11(ZN)/XCG11(N))-ONE RETURN 12 RES=DREAL(ACG12(ZN)/XCG12(N))-ONE RETURN 13 RES=DREAL(ACG13(ZN)/XCG13(N))-ONE RETURN 14 RES=DREAL(ACG14(ZN)/XCG14(N))-ONE RETURN 15 RES=DREAL(ACG15(ZN)/XCG15(N))-ONE RETURN 16 RES=DREAL(ACG16(ZN)/XCG16(N))-ONE RETURN 17 RES=DREAL(ACG17(ZN)/XCG17(N))-ONE RETURN 18 RES=DREAL(ACG18(ZN)/XCG18(N))-ONE RETURN 19 RES=DREAL(ACG19(ZN)/XCG19(N))-ONE RETURN 20 RES=DREAL(ACG20(ZN)/XCG20(N))-ONE RETURN 21 RES=DREAL(ACG21(ZN)/XCG21(N))-ONE RETURN 22 RES=DREAL(ACG22(ZN)/XCG22(N))-ONE RETURN 23 RES=DREAL(ACG23(ZN)/XCG23(N))-ONE RETURN 24 RES=DREAL(ACG24(ZN)/XCG24(N))-ONE RETURN 25 RES=DREAL(ACG25(ZN)/XCG25(N))-ONE RETURN 26 CONTINUE RES=DREAL(ACG26(ZN)/XCG26(N))-ONE RETURN END SUBROUTINE INVERS(X,I,RES,F1) * ----------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- CALCULATE THE RELATIVE ACCURACY OF THE MELLIN INVERSION USING C--- THE ANALYTIC CONTINUATION ACGi VS THE NUMERICAL REPRESENTATION C--- OF THE BASUC FUNCTIONS FKNi C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 DIR,STA,SS,ZN,FF,FUNC * COMMON /OFFS / CP(26) COMMON /PI / PI COMMON /WGAUSS/ XL8(8),WL8(8),XL32(32),WL32(32) COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON /FKNLL/ LL COMMON /ZET2/ ZETA2 COMMON /ZET3/ ZETA3 * DIMENSION ZINT(51) * LL = I IGAUSS = 8 ZERO=0.0D0 * CPAR=CP(I) IF(X.LE.0.7D0) RANGE=71.0D0 IF(X.LE.0.7D0) RANGE=71.0D0 IF(X.LE.0.7D0) INTE =20 IF(X.GT.0.7D0) INTE =20 IF(X.LE.0.7D0) PHI=3.0D0/4.0D0*PI IF(X.GT.0.7D0) PHI=7.0D0/8.0D0*PI IF(X.GT.0.98D0) PHI=19.0D0/20.0D0*PI DIR=DCMPLX(DCOS(PHI),DSIN(PHI)) STA=DCMPLX(CPAR,ZERO) ST =EXP(LOG(RANGE)/DBLE(INTE)) ST0 =1.0D0 ZINT(1)=ZERO DO 10 L=1,20 ST0 =ST0*ST L1=L+1 ZINT(L1)=ST0-1.0D0 10 CONTINUE C SS=DCMPLX(ZERO,ZERO) XBL=LOG(X) * DO 20 L=1,20 A=ZINT(L) B=ZINT(L+1) DLI=(B-A)/2.0D0 SLI=(B+A)/2.0D0 * IF(IGAUSS.EQ. 8) NM=8 IF(IGAUSS.EQ.32) NM=32 IF(IGAUSS.NE.8.AND.IGAUSS.NE.32) &WRITE(6,*) '*** IGAUSS=',IGAUSS,'*** WRONG IN SR INVERSE, STOP' IF(IGAUSS.NE.8.AND.IGAUSS.NE.32) STOP * DO 21 M=1,NM IF(IGAUSS.EQ. 8) W=WL8(M) IF(IGAUSS.EQ.32) W=WL32(M) IF(IGAUSS.EQ. 8) ZZ=XL8(M) IF(IGAUSS.EQ.32) ZZ=XL32(M) Z= DLI*ZZ+SLI ZN=STA+Z*DIR FF=FUNC(ZN) SS=SS+FF*DIR*EXP(-XBL*ZN)*W*DLI 21 CONTINUE * 20 CONTINUE * F=DIMAG(SS)/PI F1=FUNO(X) RES=F/F1-1.0D0 1 CONTINUE * 100 CONTINUE * RETURN END SUBROUTINE INV1(X,I,F2) * ----------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- CALCULATE THE MELLIN INVERSION USING C--- THE ANALYTIC CONTINUATION ACGi C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 DIR,STA,SS,ZN,FF,FUNC * COMMON /OFFS / CP(26) COMMON /PI / PI COMMON /WGAUSS/ XL8(8),WL8(8),XL32(32),WL32(32) COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON /FKNLL/ LL COMMON /ZET2/ ZETA2 COMMON /ZET3/ ZETA3 * DIMENSION ZINT(51) * LL = I IGAUSS = 8 ZERO=0.0D0 * CPAR=CP(I) IF(X.LE.0.7D0) RANGE=71.0D0 IF(X.LE.0.7D0) RANGE=71.0D0 IF(X.LE.0.7D0) INTE =20 IF(X.GT.0.7D0) INTE =20 IF(X.LE.0.7D0) PHI=3.0D0/4.0D0*PI IF(X.GT.0.7D0) PHI=7.0D0/8.0D0*PI IF(X.GT.0.98D0) PHI=19.0D0/20.0D0*PI DIR=DCMPLX(DCOS(PHI),DSIN(PHI)) STA=DCMPLX(CPAR,ZERO) ST =EXP(LOG(RANGE)/DBLE(INTE)) ST0 =1.0D0 ZINT(1)=ZERO DO 10 L=1,20 ST0 =ST0*ST L1=L+1 ZINT(L1)=ST0-1.0D0 10 CONTINUE C SS=DCMPLX(ZERO,ZERO) XBL=LOG(X) * DO 20 L=1,20 A=ZINT(L) B=ZINT(L+1) DLI=(B-A)/2.0D0 SLI=(B+A)/2.0D0 * IF(IGAUSS.EQ. 8) NM=8 IF(IGAUSS.EQ.32) NM=32 IF(IGAUSS.NE.8.AND.IGAUSS.NE.32) &WRITE(6,*) '*** IGAUSS=',IGAUSS,'*** WRONG IN SR INVERSE, STOP' IF(IGAUSS.NE.8.AND.IGAUSS.NE.32) STOP * DO 21 M=1,NM IF(IGAUSS.EQ. 8) W=WL8(M) IF(IGAUSS.EQ.32) W=WL32(M) IF(IGAUSS.EQ. 8) ZZ=XL8(M) IF(IGAUSS.EQ.32) ZZ=XL32(M) Z= DLI*ZZ+SLI ZN=STA+Z*DIR FF=FUNC(ZN) SS=SS+FF*DIR*EXP(-XBL*ZN)*W*DLI 21 CONTINUE * 20 CONTINUE * F=DIMAG(SS)/PI F2=F 1 CONTINUE * 100 CONTINUE * RETURN END REAL*8 FUNCTION FUNO(X) * ----------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- SELECTION ROUTINE FOR: FKNi C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMMON /FKNLL/ LL * GOTO(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22, & 23,24,25,26), LL 1 F=FKN1(X) GOTO 1000 2 F=FKN2(X) GOTO 1000 3 F=FKN3(X) GOTO 1000 4 F=FKN4(X) GOTO 1000 5 F=FKN5(X) GOTO 1000 6 F=FKN6(X) GOTO 1000 7 F=FKN7(X) GOTO 1000 8 F=FKN8(X) GOTO 1000 9 F=FKN9(X) GOTO 1000 10 F=FKN10(X) GOTO 1000 11 F=FKN11(X) GOTO 1000 12 F=FKN12(X) GOTO 1000 13 F=FKN13(X) GOTO 1000 14 F=FKN14(X) GOTO 1000 15 F=FKN15(X) GOTO 1000 16 F=FKN16(X) GOTO 1000 17 F=FKN17(X) GOTO 1000 18 F=FKN18(X) GOTO 1000 19 F=FKN19(X) GOTO 1000 20 F=FKN20(X) GOTO 1000 21 F=FKN21(X) GOTO 1000 22 F=FKN22(X) GOTO 1000 23 F=FKN23(X) GOTO 1000 24 F=FKN24(X) GOTO 1000 25 F=FKN25(X) GOTO 1000 26 F=FKN26(X) * 1000 FUNO=F * RETURN END COMPLEX*16 FUNCTION FUNC(Z) * --------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- SELECTION ROUTINE FOR: ACGi C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) COMMON /FKNLL/ LL * Z1=Z-1.0D0 * GOTO(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22, & 23,24,25,26), LL 1 F=ACG1(Z1) GOTO 1000 2 F=ACG2(Z1) GOTO 1000 3 F=ACG3(Z1) GOTO 1000 4 F=ACG4(Z1) GOTO 1000 5 F=ACG5(Z1) GOTO 1000 6 F=ACG6(Z1) GOTO 1000 7 F=ACG7(Z1) GOTO 1000 8 F=ACG8(Z1) GOTO 1000 9 F=ACG9(Z1) GOTO 1000 10 F=ACG10(Z1) GOTO 1000 11 F=ACG11(Z1) GOTO 1000 12 F=ACG12(Z1) GOTO 1000 13 F=ACG13(Z1) GOTO 1000 14 F=ACG14(Z1) GOTO 1000 15 F=ACG15(Z1) GOTO 1000 16 F=ACG16(Z1) GOTO 1000 17 F=ACG17(Z1) GOTO 1000 18 F=ACG18(Z1) GOTO 1000 19 F=ACG19(Z1) GOTO 1000 20 F=ACG20(Z1) GOTO 1000 21 F=ACG21(Z1) GOTO 1000 22 F=ACG22(Z1) GOTO 1000 23 F=ACG23(Z1) GOTO 1000 24 F=ACG24(Z1) GOTO 1000 25 F=ACG25(Z1) GOTO 1000 26 F=ACG26(Z1) * 1000 FUNC=F * RETURN END SUBROUTINE ACEND C ---------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C END OF THE CODE: ANCONT C C************************************************************************ C C CALL UOUT C WRITE(6,*) '***** ANCONT COMPLETED *****' C RETURN END COMPLEX*16 FUNCTION ACG1(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1+X)/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK2,DL,ZERO,ONE C COMMON/ACLOG2/ AK2(10) COMMON/ACCON1/ DL COMMON/VAL / ZERO,ONE C T=DCMPLX(ZERO,ZERO) DO 1 L=2,11 K=L-1 T=T+AK2(K)/(ZN+DBLE(K+1)) 1 CONTINUE C ACG1=(DL*DL- ZN*T)/2.0D0 C RETURN END COMPLEX*16 FUNCTION ACG2(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1+X)**2/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK3,DL,ZERO,ONE C COMMON/ACLOG3/ AK3(11) COMMON/ACCON1/ DL COMMON/VAL / ZERO,ONE C T=DCMPLX(ZERO,ZERO) DO 1 L=3,13 K=L-2 T=T+AK3(K)/(ZN+DBLE(K+2)) 1 CONTINUE C ACG2=(DL**3- ZN*T)/3.0D0 C RETURN END COMPLEX*16 FUNCTION ACG3(ZN1) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI2(X)/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,DL,ZERO,ONE,ZET2,GE C COMMON/ACLOG1/ AK1(9) COMMON/IAPP / IAPP COMMON/VAL / ZERO,ONE COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/ACCON4/ GE C ZN=ZN1+ONE C IF(IAPP.EQ.1) GOTO 10 IF(IAPP.EQ.2) GOTO 20 IF(IAPP.EQ.3) GOTO 30 WRITE(6,*) '*** ERROR IN ACG3, IAPP=',IAPP,' WRONG, STOP ***' STOP C 10 T=DCMPLX(DL*ZET2,ZERO) Z=ZN1 Z1=Z+ONE DO 1 L=1,9 ZL =DCMPLX(DBLE(L),ZERO) ZL1=Z+ZL+ONE CALL PSI0(ZL1,PS) S1=PS+GE T=T-AK1(L)*(ZET2*Z/(Z+ZL)+ZL/(Z+ZL)**2*S1) 1 CONTINUE GOTO 100 C 20 T=1.01/(ZN+ONE)-0.846/(ZN+ONE*2)+1.155/(ZN+ONE*3) & -1.074/(ZN+ONE*4)+0.55/(ZN+ONE*5) GOTO 100 30 T=1.004/(ZN+ONE)-0.846/(ZN+ONE*2)+1.342/(ZN+ONE*3) & -1.532/(ZN+ONE*4)+0.839/(ZN+ONE*5) 100 CONTINUE ACG3=T C RETURN END COMPLEX*16 FUNCTION ACG4(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI2(-X)/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,DL,ZERO,ONE,ZET2 C COMMON/ACLOG1/ AK1(9) COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/VAL / ZERO,ONE C T=DCMPLX(-ZET2/2.0D0*DL,ZERO) C DO 1 L=1,9 ZL =DCMPLX(DBLE(L),ZERO) ZNL =ZN+ZL ZNL1=ZNL+DCMPLX(ONE,ZERO) CALL BET(ZNL1,V1) C T=T+AK1(L)*(ZN/ZNL*ZET2/2.0D0+ZL/ZNL**2*(DL-V1)) 1 CONTINUE C ACG4=T C RETURN END COMPLEX*16 FUNCTION ACG5(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(X) LI2(X)/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,ZERO,ONE,DL,ZET2,GE C COMMON/ACLOG1/ AK1(9) COMMON/VAL / ZERO,ONE COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/ACCON4/ GE C T=DCMPLX(ZERO,ZERO) Z=ZN DO 1 L=1,9 ZL =DCMPLX(DBLE(L),ZERO) ZNL=Z+ZL ZL1=ZNL+ONE CALL PSI0(ZL1,PS) CALL PSI1(ZL1,S1P) S1=PS+GE T=T-AK1(L)*ZL/ZNL**2*(ZET2+S1P-2.0D0*S1/ZNL) 1 CONTINUE C ACG5=T C RETURN END COMPLEX*16 FUNCTION ACG6(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI3(X)/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,DL,ZERO,ONE,ZET3,GE,ZET2 C COMMON/ACLOG1/ AK1(9) COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C T=DCMPLX(DL*ZET3,ZERO) DO 1 L=1,9 ZL=DCMPLX(DBLE(L),ZERO) ZNL=ZN+ZL ZNL1=ZNL+ONE CALL PSI0(ZNL1,V1) S1=V1+GE C T=T-AK1(L)*(ZN/ZNL*ZET3+ZL/ZNL**2*(ZET2-S1/ZNL)) 1 CONTINUE C ACG6=T C RETURN END COMPLEX*16 FUNCTION ACG7(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI3(-X)/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,DL,ZERO,ONE,ZET2,ZET3 C COMMON/ACLOG1/ AK1(9) COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/VAL / ZERO,ONE C T=DCMPLX(-3.0D0*ZET3/4.0D0*DL,ZERO) C DO 1 L=1,9 ZL =DCMPLX(DBLE(L),ZERO) ZNL =ZN+ZL ZNL1=ZNL+DCMPLX(ONE,ZERO) CALL BET(ZNL1,V1) C T=T+AK1(L)*(ZN/ZNL*3.0D0*ZET3/4.0D0+ZL/ZNL**2/2.0D0*ZET2 & -ZL/ZNL**3*(DL-V1)) 1 CONTINUE C ACG7=T C RETURN END COMPLEX*16 FUNCTION ACG8(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: S12(X)/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,DL,ZERO,ONE,ZET2,GE,ZET3 C COMMON/ACLOG1/ AK1(9) COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C T=DCMPLX(ZERO,ZERO) DO 1 L=1,9 ZL=DCMPLX(DBLE(L),ZERO) ZNL=ZN+ZL ZNL1=ZNL+ONE CALL PSI0(ZNL1,PS0) CALL PSI1(ZNL1,PS1) S1=PS0+GE S2=ZET2-PS1 T=T-AK1(L)*(ZN*ZET3/ZNL+ZL/ZNL**2/2.0D0*(S1**2+S2)) 1 CONTINUE C ACG8=T+DL*ZET3 C RETURN END COMPLEX*16 FUNCTION ACG9(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: S12(-X)/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,AK2,AK3,DL,ZERO,ONE,ZET3 C COMMON/ACLOG1/ AK1(9) COMMON/ACLOG2/ AK2(10) COMMON/ACLOG3/ AK3(11) COMMON/ACCON1/ DL COMMON/ACCON3/ ZET3 COMMON/VAL / ZERO,ONE C T=DCMPLX(ZET3*DL/8.0D0,ZERO) DO 1 K=1,9 T1=DCMPLX(ZERO,ZERO) DO 2 L=2,11 L1=L-1 ZNKL=ZN+DCMPLX(DBLE(K+L),ZERO) T1=T1+AK2(L1)/ZNKL 2 CONTINUE ZK=DCMPLX(DBLE(K),ZERO) ZNK=ZN+ZK T=T-AK1(K)*ZN/ZNK*(ZET3/8.0D0-T1/2.0D0) 1 CONTINUE T2=DCMPLX(ZERO,ZERO) DO 3 K=3,13 L=K-2 ZK=DCMPLX(DBLE(K),ZERO) ZNK=ZN+ZK T2=T2+AK3(L)/ZNK 3 CONTINUE T=T-T2/2.0D0 C ACG9=T C RETURN END COMPLEX*16 FUNCTION ACG10(ZN) C ----------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: I1(X)/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,AK2,DL,ZERO,ONE,ZET3,GE C COMMON/ACLOG1/ AK1(9) COMMON/ACLOG2/ AK2(10) COMMON/ACCON1/ DL COMMON/ACCON4/ GE COMMON/ACCON3/ ZET3 COMMON/VAL / ZERO,ONE C T=DCMPLX(-5.0D0/8.0D0*ZET3*DL,ZERO) C DO 1 K=2,11 L=K-1 ZNK=ZN+DBLE(K) ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) S1=PS+GE T=T+AK2(L)*S1/ZNK 1 CONTINUE DO 2 K=1,9 ZNK=ZN+DBLE(K) T2=DCMPLX(ZERO,ZERO) DO 3 L=1,9 ZNKL=ZNK+DBLE(L) ZNKL1=ZNKL+ONE CALL PSI0(ZNKL1,PS1) S2=PS1+GE T2=T2-AK1(L)*S2/ZNKL 3 CONTINUE T=T+AK1(K)*ZN/ZNK*(5.0D0/8.0D0*ZET3+T2) 2 CONTINUE C ACG10=T C RETURN END COMPLEX*16 FUNCTION ACG11(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1-X)/(1+X) LI2(X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,CK1,P21,DL,ZERO,ONE,ZET2,GE,ZET3 C COMMON/ACLOG1/ AK1(9) COMMON/ACLOG6/ CK1(12) COMMON/POLY1 / P21(4) COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C T=DCMPLX(ZERO,ZERO) T1=DCMPLX((-ZET2+DL**2)/2.0D0,ZERO) T2=DCMPLX(7.0D0/4.0D0*ZET3-ZET2*DL+DL**3/3.0D0,ZERO) C DO 1 K=1,12 L=K-1 U2=T1 ZK=DCMPLX(DBLE(L)) C DO 2 M=1,9 ZM=DCMPLX(DBLE(M)) ZM1=ZM+ONE ZNM=ZN+ZM+ZK ZNM1=ZNM+ONE CALL PSI0(ZNM1,PS) CALL PSI0(ZM1,PS1) S1=PS+GE S11=PS1+GE U2=U2-AK1(M)*(ZM/ZNM*S1-S11) 2 CONTINUE C T=T+CK1(K)*U2 1 CONTINUE C DO 3 K=1,4 L=K-1 C U3=T2 ZK=DCMPLX(DBLE(L),ZERO) DO 4 M=1,9 ZM=DCMPLX(DBLE(M),ZERO) ZM1=ZM+ONE ZMN=ZN+ZK+ZM ZMN1=ZMN+ONE CALL PSI0(ZMN1,PS5) CALL PSI1(ZMN1,PS2) CALL PSI0(ZM1,PS3) CALL PSI1(ZM1,PS4) S1=PS5+GE S2=-PS2+ZET2 S11=PS3+GE S21=-PS4+ZET2 U3=U3+AK1(M)*(ZM/ZMN*(S1**2+S2)-(S11**2+S21)) 4 CONTINUE T=T+P21(K)*U3 3 CONTINUE C ACG11=T C RETURN END COMPLEX*16 FUNCTION ACG12(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1-X)/(1+X)*LI2(-X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,AK2,DL,ZERO,ONE,GE C COMMON/ACLOG1/ AK1(9) COMMON/ACLOG2/ AK2(10) COMMON/ACCON1/ DL COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C T=DCMPLX(ZERO,ZERO) DO 1 K=1,9 ZK=DCMPLX(DBLE(K),ZERO) T2=DCMPLX(ZERO,ZERO) ZNK=ZN+ZK DO 2 L=2,11 L1=L-1 ZNKL=ZNK+DBLE(L) T2=T2+AK2(L1)*ZNK/ZNKL 2 CONTINUE ZNK1=ZNK+ONE CALL BET(ZNK1,U1) CALL PSI0(ZNK1,U2) V1=U1*(U2+GE-DL) CALL BET1(ZNK1,V2) C RES=-ONE/2.0D0*(DL**2-T2)+V2-V1 T=T-AK1(K)/ZK*RES 1 CONTINUE C ACG12=T C RETURN END COMPLEX*16 FUNCTION ACG13(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1+X)/(1+X)*LI2(-X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK2,AK3,DL,ZERO,ONE,ZET2 C COMMON/ACLOG2/ AK2(10) COMMON/ACLOG3/ AK3(11) COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/VAL / ZERO,ONE C T0=DCMPLX(-1.0D0/4.0D0*ZET2*DL**2,ZERO) C T1=DCMPLX(ZERO,ZERO) DO 1 L=3,13 K=L-2 T1=T1+AK3(K)/(ZN+DBLE(L)) 1 CONTINUE C T2=DCMPLX(ZERO,ZERO) DO 2 L=2,11 K=L-1 ZNK1=ZN+DBLE(L+1) CALL BET(ZNK1,V1) T2=T2+AK2(K)*ZN/(ZN+DBLE(L))*(ZET2/2.0D0-(DL-V1)/(ZN+DBLE(L))) 2 CONTINUE C ACG13=T0+(T1+T2)/2.0D0 C RETURN END COMPLEX*16 FUNCTION ACG14(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LOG^2(1+X)-LOG^2(2))/(X-1) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 BK2,ZERO,ONE C COMMON/ACLOG5/ BK2(10) COMMON/VAL / ZERO,ONE C T=DCMPLX(ZERO,ZERO) DO 1 L=1,10 ZNL=ZN+DBLE(L) T=T+BK2(L)/ZNL 1 CONTINUE C ACG14=T C RETURN END COMPLEX*16 FUNCTION ACG15(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LOG(1+x)-LOG(2))/(X-1)*LI2(X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 BK1,ZERO,ONE,ZET2,GE C COMMON/ACLOG4/ BK1(9) COMMON/ACCON2/ ZET2 COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C T=ZERO DO 1 L=1,9 ZNK=ZN+DCMPLX(DBLE(L),ZERO) ZNK2=ZNK+ONE CALL PSI0(ZNK2,PS) S1=PS+GE T=T+BK1(L)/ZNK*(ZET2-S1/ZNK) 1 CONTINUE C ACG15= T C RETURN END COMPLEX*16 FUNCTION ACG16(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LOG(1+x)-LOG(2))/(X-1)*LI2(-X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 BK1,ZERO,ONE,ZET2,DL C COMMON/ACLOG4/ BK1(9) COMMON/ACCON2/ ZET2 COMMON/ACCON1/ DL COMMON/VAL / ZERO,ONE C T=ZERO DO 1 L=1,9 ZNK=ZN+DCMPLX(DBLE(L),ZERO) ZNK2=ZNK+ONE CALL BET(ZNK2,V1) T1=DL-V1 T=T+BK1(L)/ZNK*(-ZET2/2.0D0+T1/ZNK) 1 CONTINUE C ACG16= T C RETURN END COMPLEX*16 FUNCTION ACG17(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(X) LOG^2(1+X)/(X-1) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK2,ZERO,ONE,ZET2 C COMMON/ACLOG2/ AK2(10) COMMON/VAL / ZERO,ONE COMMON/ACCON2/ ZET2 C T=DCMPLX(ZERO,ZERO) DO 1 K=2,11 L=K-1 ZNK1=ZN+DBLE(K+1) CALL PSI1(ZNK1,V1) T=T+AK2(L)*V1 1 CONTINUE C ACG17=T C RETURN END COMPLEX*16 FUNCTION ACG18(ZN) C ----------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI2(X)-ZETA2)/(X-1) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 CK1,P21,ZERO,ONE,ZET2,ZET3,GE C COMMON/ACLOG6/ CK1(12) COMMON/POLY1 / P21(4) COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C ZN1=ZN+ONE T=DCMPLX(ZERO,ZERO) C CALL PSI0(ZN1,PS1) CALL PSI1(ZN1,PS2) SPS1=PS1+GE SPS2=-PS2+ZET2 T=T+(SPS1**2+SPS2)/ZN-ZET2*SPS1 C DO 1 L=1,12 ZNK1=ZN+DBLE(L-1) ZNK2=ZNK1+ONE CALL PSI0(ZNK2,PS) S1=PS+GE T=T+CK1(L)*S1/ZNK1*ZN 1 CONTINUE C DO 2 L=1,4 ZNK1=ZN+DBLE(L-1) ZNK2=ZNK1+ONE CALL PSI0(ZNK2,PS) CALL PSI1(ZNK2,PS1) S1=PS+GE S2=-PS1+ZET2 T=T-P21(L)*(S1**2+S2)/ZNK1*ZN 2 CONTINUE C ACG18=T C RETURN END COMPLEX*16 FUNCTION ACG19(ZN) C ----------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI2(-X)+ZETA2/2)/(X-1) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,ZERO,ONE,ZET2,GE C COMMON/ACLOG1/ AK1(9) COMMON/ACCON2/ ZET2 COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C T=DCMPLX(ZERO,ZERO) ZN1=ZN+ONE CALL PSI0(ZN1,PS) S1=PS+GE T=T+S1*ZET2/2.0D0 DO 1 L=1,9 ZK=DCMPLX(DBLE(L)) ZNK1=ZN+ZK+ONE CALL PSI0(ZNK1,PS) S1=PS+GE T=T-AK1(L)*S1/ZK 1 CONTINUE C ACG19=T C RETURN END COMPLEX*16 FUNCTION ACG20(ZZ) C ----------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI3(X)-ZETA3)/(X-1) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 DL,ZERO,ONE,ZET2,ZET3,GE,P24,P34,P22,CK2,CK4 C COMMON/ACLOG7/ CK2(13) COMMON/ACLOG9/ CK4(13) COMMON/POLY2 / P22(4) COMMON/POLY4 / P24(5),P34(5) COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C T=DCMPLX(ZET2**2/2.0D0,ZERO) C ZN = ZZ ZN1=ZN+ONE CALL PSI0(ZN1,PS) S1=PS+GE T=T-ZET3*S1 C DO 1 K=1,13 L=K-1 ZNK=ZN+DBLE(L) ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) S1=PS+GE R=ZN/ZNK C T=T+CK2(K)*R*S1 1 CONTINUE C DO 3 K=1,4 L=K-1 ZNK=ZN+DBLE(L) ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) CALL PSI1(ZNK1,PS1) S1=PS+GE S2=-PS1+ZET2 R=ZN/ZNK T1=S1**2+S2 C T=T-P22(K)*R*T1 3 CONTINUE C DO 4 K=1,13 L=K-1 ZNK=ZN+DBLE(L) ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) S1=PS+GE C T=T-CK4(K)/ZNK*ZN/2.0D0 4 CONTINUE C DO 5 K=1,5 L=K-1 ZNK=ZN+DBLE(L) ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) CALL PSI1(ZNK1,PS1) S1=PS+GE S2=-PS1+ZET2 T1=-S1/ZNK T2=(S1**2+S2)/ZNK C T=T-(P24(K)*T1+P34(K)*T2)*ZN/2.0D0 5 CONTINUE C C ACG20=T C RETURN END COMPLEX*16 FUNCTION ACG21(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (S12(X)-ZETA3)/(X-1) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 ZERO,ONE,ZET2,ZET3,GE,CK3,P23,P33 C COMMON/ACLOG8/ CK3(10) COMMON/POLY3 / P23(5),P33(5) COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C T=DCMPLX(ZERO,ZERO) ZN1=ZN+ONE CALL PSI0(ZN1,PS) CALL PSI1(ZN1,PS1) CALL PSI2(ZN1,PS2) S1=PS+GE S2=-PS1+ZET2 S3= PS2/2.0D0+ZET3 C T=T-ZET3*S1 T=T+(S1**3+3.0D0*S1*S2+2.0D0*S3)/2.0D0/ZN C DO 1 K=1,10 L=K-1 ZNK=ZN+DBLE(L) ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) S1=PS+GE T=T+CK3(K)*S1*ZN/ZNK 1 CONTINUE C DO 2 K=1,5 L=K-1 ZNK=ZN+DBLE(L) ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) CALL PSI1(ZNK1,PS1) CALL PSI2(ZNK1,PS2) S1=PS+GE S2=-PS1+ZET2 S3= PS2/2.0D0+ZET3 T2=S1**2+S2 T3=S1**3+3.0D0*S1*S2+2.0D0*S3 T=T+ZN/ZNK*(P33(K)*T3-P23(K)*T2) 2 CONTINUE C ACG21=T C RETURN END COMPLEX*16 FUNCTION ACG22(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(X) LI2(X)/(X-1) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 CK1,P21,GE,ZERO,ONE C COMMON/ACLOG6/ CK1(12) COMMON/POLY1 / P21(4) COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C T=DCMPLX(ZERO,ZERO) C DO 1 L=1,12 ZNK1=ZN+DBLE(L) CALL PSI1(ZNK1,PS1) T=T+CK1(L)*PS1 1 CONTINUE C DO 2 L=1,4 ZNK1=ZN+DBLE(L) CALL PSI0(ZNK1,PS) CALL PSI1(ZNK1,PS1) CALL PSI2(ZNK1,PS2) TA=(PS+GE)*PS1-PS2/2.0D0 T=T-P21(L)*TA 2 CONTINUE C ACG22=T C RETURN END COMPLEX*16 FUNCTION ACG23(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI3(-X)+3/4*ZETA3)/(X-1) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,GE,ZERO,ONE,ZET2,ZET3,XLI4,DL C COMMON/ACLOG1/ AK1(9) COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/ACCON5/ XLI4 COMMON/VAL / ZERO,ONE C C >>> M[Li3(x)/(1+x)](N) C U=ACG6(ZN) C T=DCMPLX(ZERO,ZERO) T=T-ZET2**2/2.0D0+ZET3*DL ZN1=ZN+ONE CALL PSI0(ZN1,PS) S1=PS+GE T=T+3.0D0/4.0D0*ZET3*S1-U DO 1 L=1,9 ZK=DCMPLX(DBLE(L),ZERO) ZNK=ZN+ZK ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) S1=PS+GE R=ZN/ZNK H=ZET3-ZET2/ZNK-ZET2/ZK+ & S1*(1.0D0/ZNK**2+1.0D0/ZK**2+1.0D0/ZNK/ZK) T=T-AK1(L)*R*H 1 CONTINUE C ACG23=T C RETURN END COMPLEX*16 FUNCTION ACG24(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (I1(X)+5/8*ZETA3)/(X-1) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,CK5,DK5,DL,ZERO,ONE,ZET3,GE,ZET2 C COMMON/ACLOG1/ AK1(9) COMMON/ACLG10/ CK5(9) COMMON/ACLG11/ DK5(10) COMMON/ACCON1/ DL COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C T=DCMPLX(-2.0D0*ZET3*DL,ZERO) C C >>> M[S12(x)/(1+x)](N) C U=ACG8(ZN) C T=T+2.0D0*U ZN1=ZN+ONE CALL PSI0(ZN1,PS) S1=PS+GE T=T+5.0D0/8.0D0*ZET3*S1 C DO 1 L=1,9 ZNK=ZN+DBLE(L) ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) CALL PSI1(ZNK1,PS1) S1=PS+GE S2=-PS1+ZET2 T1=ZN/ZNK*(2.0D0*ZET3-(S1**2+S2)/ZNK) T=T+AK1(L)*T1 1 CONTINUE C DO 2 L=1,9 ZNK=ZN+DBLE(L) ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) S1=PS+GE T=T+CK5(L)*S1/ZNK*ZN 2 CONTINUE C DO 3 K=1,10 L=K-1 ZNK=ZN+DBLE(L) ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) CALL PSI1(ZNK1,PS1) S1=PS+GE S2=-PS1+ZET2 T1=ZN/ZNK*(S1**2+S2) T=T-DK5(K)*T1 3 CONTINUE C ACG24=T C RETURN END COMPLEX*16 FUNCTION ACG25(ZN) C ---------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (S12(-X) -ZETA3/8)/(X-1) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) C REAL*8 AK1,AK2,GE,DL,ZET3,ZERO,ONE C COMMON/ACLOG1/ AK1(9) COMMON/ACLOG2/ AK2(10) COMMON/ACCON1/ DL COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/VAL / ZERO,ONE C C >>> M[I1(x)/(1+x)](N) C U=ACG10(ZN) C T=DCMPLX(5.0D0/16.0D0*ZET3*DL,ZERO)+U/2.0D0 ZN1=ZN+ONE CALL PSI0(ZN1,PS) S1=PS+GE T=T-ZET3/8.0D0*S1 C DO 1 L=2,11 K=L-1 ZK=DCMPLX(DBLE(L),ZERO) ZNK=ZN+ZK ZNK1=ZNK+ONE CALL PSI0(ZNK1,PS) S1=PS+GE T=T+AK2(K)*S1/ZK/ZNK*ZN/2.0D0 1 CONTINUE C CO=-5.0D0/8.0D0*ZET3 C DO 2 K=1,9 ZK=DCMPLX(DBLE(K),ZERO) ZNK=ZN+ZK T1=CO DO 3 L=1,9 ZNKL=ZN+DBLE(K+L) ZNKL1=ZNKL+ONE CALL PSI0(ZNKL1,PS) S1=PS+GE T1=T1+AK1(L)*S1/ZNKL 3 CONTINUE T=T+AK1(K)/ZNK*ZN/2.0D0*T1 2 CONTINUE C ACG25=T C RETURN END COMPLEX*16 FUNCTION ACG26(ZN) C ----------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG^3(1-X)/(1+X) C--- FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT COMPLEX*16 (A-H,O-Z) REAL*8 AK1,ZERO,ONE,XLI4,ZET2,ZET3,GE C COMMON/ACLOG1/ AK1(9) COMMON/ACCON2/ ZET2 COMMON/ACCON3/ ZET3 COMMON/ACCON4/ GE COMMON/ACCON5/ XLI4 COMMON/VAL / ZERO,ONE C T=DCMPLX(-6.0D0*XLI4,ZERO) DO 1 K=1,9 ZK=DCMPLX(DBLE(K),ZERO) ZK1=ZK+ONE ZKN=ZK+ZN ZKN1=ZKN+ONE CALL PSI0(ZKN1,PS) CALL PSI1(ZKN1,PS1) CALL PSI2(ZKN1,PS2) S1=PS+GE S2=-PS1+ZET2 S3= PS2/2.0D0+ZET3 CALL PSI0(ZK1,PS) CALL PSI1(ZK1,PS1) CALL PSI2(ZK1,PS2) H1=PS+GE H2=-PS1+ZET2 H3= PS2/2.0D0+ZET3 T=T-AK1(K)*(ZK/ZKN*(S1**3+3.0D0*S1*S2+2.0D0*S3) & -(H1**3+3.0D0*H1*H2+2.0D0*H3)) 1 CONTINUE C ACG26=T C RETURN END DOUBLE PRECISION FUNCTION FLI2(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- LI2(X) C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C EXTERNAL FR1 C PI = 3.141592653589793238462643D0 ZETA2 = PI**2/6.0D0 C IF(X.LT.-1.0D0.OR.X.GT.1.0D0) GOTO 100 IF(X.EQ.1.0D0) GOTO 5 IF(X.EQ.-1.0D0) GOTO 6 IF(X.LT.0.0D0) GOTO 1 IF(X.EQ.0.0D0) GOTO 2 IF(X.GT.0.5D0) GOTO 3 T=FR1(X) GOTO 200 100 WRITE(6,*) 'FLI2 -> NOT ALLOWED,X=',X,'STOP ***' STOP 1 Y=-X IF(Y.GT.0.5D0) GOTO 4 Y2=Y**2 T=FR1(Y2)/2.0D0-FR1(Y) GOTO 200 2 T=0.0D0 GOTO 200 3 XM=1.0D0-X T=-FR1(XM)-LOG(X)*LOG(XM)+ZETA2 GOTO 200 4 YM=1.0D0-Y T1=-FR1(YM)-LOG(Y)*LOG(YM)+ZETA2 Y2=Y**2 IF(Y2.LT.0.5) THEN T2=FR1(Y2) ELSE T2=-FR1(1.0D0-Y2)-LOG(Y2)*LOG(1.0D0-Y2)+ZETA2 ENDIF T=T2/2.0D0-T1 GOTO 200 5 T=ZETA2 GOTO 200 6 T=-ZETA2/2.0D0 GOTO 200 C 200 FLI2=T C RETURN END DOUBLE PRECISION FUNCTION FR1(X) C -------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- SUBSIDIARTY ROUTINE FOR LI2(X) C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C Y=LOG(1.0D0-X) Y2=Y*Y C T = (-1.D0+(-1.D0/4.D0+(-1.D0/36.D0+(1.D0/3600.D0+( &-1.D0/211680.D0+(1.D0/10886400.D0+(-1.D0/526901760.D0 &+(691.D0/16999766784000.D0+(-1.D0/1120863744000.D0 &+3617.D0/0.18140058832896D18*Y2)*Y2)*Y2)*Y2)*Y2)*Y2) &*Y2)*Y)*Y)*Y C FR1=T C RETURN END SUBROUTINE GAMMAL(ZZ,RES) C ------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- LOG(GAMMA(Z)) FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 T1,T2,ZZ,Z,X,X2,RES C Z=ZZ PI = 3.141592653589793238462643D0 C ONE=DCMPLX(1.0D0,0.0D0) T=DCMPLX(0.0D0,0.0D0) 2 R=SQRT(DREAL(Z)**2+DIMAG(Z)**2) IF(R.GT.10.0D0) GOTO 1 T=T-LOG(Z) Z=Z+ONE GOTO 2 1 CONTINUE C T1=Z*(LOG(Z)-1.0D0)+LOG(2.0D0*PI/Z)/2.0D0 C X=ONE/Z X2=X*X T2 = (1.D0/12.D0+(-1.D0/360.D0+(1.D0/1260.D0+(-1.D0/1680.D0+(1.D0/ #1188.D0+(-691.D0/360360.D0+(1.D0/156.D0-3617.D0/122400.D0*X2)*X2 #)*X2)*X2)*X2)*X2)*X2)*X C RES=T1+T2+T C RETURN END SUBROUTINE GAMMA(ZZ,RES) C ------------------------ C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- GAMMA(Z) FOR COMPLEX ARGUMENT C C************************************************************************ C COMPLEX*16 ZZ,T,RES C CALL GAMMAL(ZZ,T) C RES=EXP(T) C RETURN END SUBROUTINE BETA(AA,BB,RES) C -------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C--- BETA(A,B) FOR COMPLEX ARGUMENT C C************************************************************************ C COMPLEX*16 T1,T2,T3,T,RES,AA,BB C CALL GAMMAL(AA,T1) CALL GAMMAL(BB,T2) CALL GAMMAL(AA+BB,T3) T=T1+T2-T3 C RES=EXP(T) C RETURN END SUBROUTINE PSI0(ZZ,RES) C ----------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- PSI(Z) FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 Z,T,ONE,Y,T0,RES,ZZ C ONE=DCMPLX(1.0D0,0.0D0) C Z=ZZ T=DCMPLX(0.0D0,0.0D0) 2 R=SQRT(DREAL(Z)**2+DIMAG(Z)**2) IF(R.GT.10.0D0) GOTO 1 T=T-ONE/Z Z=Z+ONE GOTO 2 1 Y=ONE/Z Y2=Y*Y T0 = (-1.D0/2.D0+(-1.D0/12.D0+(1.D0/120.D0+(-1.D0/252.D0+(1.D0/240 #.D0+(-1.D0/132.D0+(691.D0/32760.D0+(-ONE/12.0D0+ONE*3617.0D0 # /8160.D0*Y2 # )*Y2 )*Y2 )*Y2 )*Y2 )*Y2 )*Y2 )*Y)*Y-LOG(Y) C RES=T+T0 C RETURN END SUBROUTINE PSI1(ZZ,RES) C ----------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- PSI'(Z) FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 Z,T,ONE,Y,T0,RES,ZZ C ONE=DCMPLX(1.0D0,0.0D0) C Z=ZZ T=DCMPLX(0.0D0,0.0D0) 2 R=SQRT(DREAL(Z)**2+DIMAG(Z)**2) IF(R.GT.10.0D0) GOTO 1 T=T+ONE/Z**2 Z=Z+ONE GOTO 2 1 Y=ONE/Z Y2=Y*Y T0 = (1.D0+(1.D0/2.D0+(1.D0/6.D0+(-1.D0/30.D0+ &(1.D0/42.D0+(-1.D0/30.D0+(5.D0/66.D0-691.D0/2730.D0*Y2) &*Y2)*Y2)*Y2)*Y2)*Y)*Y)*Y C RES=T+T0 C RETURN END SUBROUTINE PSI2(ZZ,RES) C ----------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- PSI''(Z) FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 Z,T,ONE,Y,T0,RES,ZZ C ONE=DCMPLX(1.0D0,0.0D0) TWO=ONE*2.0D0 C Z=ZZ T=DCMPLX(0.0D0,0.0D0) 2 R=SQRT(DREAL(Z)**2+DIMAG(Z)**2) IF(R.GT.10.0D0) GOTO 1 T=T-TWO/Z**3 Z=Z+ONE GOTO 2 1 Y=ONE/Z Y2=Y*Y T0 =(-1.D0+(-1.D0+(-1.D0/2.D0+(1.D0/6.D0+(-1.D0/6.D0+(3.D0/ &10.D0+(-5.D0/6.D0+691.D0/210.D0*Y2)*Y2)*Y2)*Y2)*Y2)*Y)*Y)*Y2 C RES=T+T0 C RETURN END SUBROUTINE PSI3(ZZ,RES) C ----------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- PSI'''(Z) FOR COMPLEX ARGUMENT C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 Z,T,ONE,Y,T0,RES,ZZ C ONE=DCMPLX(1.0D0,0.0D0) SIX=ONE*6.0D0 C Z=ZZ T=DCMPLX(0.0D0,0.0D0) 2 R=SQRT(DREAL(Z)**2+DIMAG(Z)**2) IF(R.GT.10.0D0) GOTO 1 T=T+SIX/Z**4 Z=Z+ONE GOTO 2 1 Y=ONE/Z Y2=Y*Y C T0 = (2.D0+(3.D0+(2.D0+(-1.D0+(4.D0/3.D0+(-3.D0+(10.D0+(-691.D0/15 #.D0+(280.D0-10851.D0/5.D0*Y2 )*Y2 )*Y2 )*Y2 )*Y2 )*Y2 )*Y2 #)*Y)*Y)*Y2*Y C RES=T+T0 C RETURN END SUBROUTINE BET(ZZ,RES) C ---------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- BET(Z) FOR COMPLEX ARGUMENT $\beta(z)$ C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 Z,ONE,RES,V1,V2,Z1,Z2,ZZ C ONE=DCMPLX(1.0D0,0.0D0) C Z=ZZ Z1=(Z+ONE)/2.0D0 Z2=Z/2.0D0 CALL PSI0(Z1,V1) CALL PSI0(Z2,V2) C RES=(V1-V2)/2.0D0 C RETURN END SUBROUTINE BET1(ZZ,RES) C ----------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- BET'(Z) FOR COMPLEX ARGUMENT $\beta'(z)$ C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 Z,ONE,RES,V1,V2,Z1,Z2,ZZ C ONE=DCMPLX(1.0D0,0.0D0) C Z=ZZ Z1=(Z+ONE)/2.0D0 Z2=Z/2.0D0 CALL PSI1(Z1,V1) CALL PSI1(Z2,V2) C RES=(V1-V2)/4.0D0 C RETURN END SUBROUTINE BET2(ZZ,RES) C ----------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- BET''(Z) FOR COMPLEX ARGUMENT $\beta''(z)$ C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 Z,ONE,RES,V1,V2,Z1,Z2,ZZ C ONE=DCMPLX(1.0D0,0.0D0) C Z=ZZ Z1=(Z+ONE)/2.0D0 Z2=Z/2.0D0 CALL PSI2(Z1,V1) CALL PSI2(Z2,V2) C RES=(V1-V2)/8.0D0 C RETURN END SUBROUTINE BET3(ZZ,RES) C ----------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- BET'''(Z) FOR COMPLEX ARGUMENT $\beta'''(z)$ C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 Z,ONE,RES,V1,V2,Z1,Z2,ZZ C ONE=DCMPLX(1.0D0,0.0D0) C Z=ZZ Z1=(Z+ONE)/2.0D0 Z2=Z/2.0D0 CALL PSI3(Z1,V1) CALL PSI3(Z2,V2) C RES=(V1-V2)/8.0D0 C RETURN END DOUBLE PRECISION FUNCTION SUM1(K,N) C ----------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- SINGLE (ALTERNATING) HARMONIC SUM C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C K1 = ABS(K) S1 = 0.0D0 C DO 10 L=1,N IF ((K. LE. 0) .AND. (MOD(L,2) .NE. 0)) THEN S1 = S1 - 1.0D0/DBLE(L)**K1 ELSE S1 = S1 + 1.0D0/DBLE(L)**K1 END IF 10 CONTINUE C SUM1 = S1 RETURN END DOUBLE PRECISION FUNCTION SUM2(J,K,N) C ------------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- DOUBLE (ALTERNATING) HARMONIC SUM C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C J1 = ABS(J) K1 = ABS(K) C S1 = 0.0D0 S2 = 0.0D0 C DO 10 L=1,N IF ((K .LE. 0) .AND. (MOD(L,2) .NE. 0)) THEN S1 = S1 - 1.0D0/DBLE(L)**K1 ELSE S1 = S1 + 1.0D0/DBLE(L)**K1 END IF IF ((J .LE. 0) .AND. (MOD(L,2) .NE. 0)) THEN S2 = S2 - S1/DBLE(L)**J1 ELSE S2 = S2 + S1/DBLE(L)**J1 END IF 10 CONTINUE C SUM2 = S2 RETURN END DOUBLE PRECISION FUNCTION SUM3(I,J,K,N) C --------------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- TRIPLE (ALTERNATING) HARMONIC SUM C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C I1 = ABS(I) J1 = ABS(J) K1 = ABS(K) C S1 = 0.0D0 S2 = 0.0D0 S3 = 0.0D0 C DO 10 L=1,N IF ((K .LE. 0) .AND. (MOD(L,2) .NE. 0)) THEN S1 = S1 - 1.0D0/DBLE(L)**K1 ELSE S1 = S1 + 1.0D0/DBLE(L)**K1 END IF IF ((J .LE. 0) .AND. (MOD(L,2) .NE. 0)) THEN S2 = S2 - S1/DBLE(L)**J1 ELSE S2 = S2 + S1/DBLE(L)**J1 END IF IF ((I .LE. 0) .AND. (MOD(L,2) .NE. 0)) THEN S3 = S3 - S2/DBLE(L)**I1 ELSE S3 = S3 + S2/DBLE(L)**I1 END IF 10 CONTINUE C SUM3 = S3 RETURN END DOUBLE PRECISION FUNCTION SUM4(I,J,K,L,N) C ----------------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- QUADRUPLE (ALTERNATING) HARMONIC SUM C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C I1 = ABS(I) J1 = ABS(J) K1 = ABS(K) L1 = ABS(L) C T1 = 0.0D0 T2 = 0.0D0 T3 = 0.0D0 T4 = 0.0D0 C DO 10 M=1,N IF ((L .LE. 0) .AND. (MOD(M,2) .NE. 0)) THEN T1 = T1 - 1.0D0/DBLE(M)**L1 ELSE T1 = T1 + 1.0D0/DBLE(M)**L1 END IF IF ((K .LE. 0) .AND. (MOD(M,2) .NE. 0)) THEN T2 = T2 - T1/DBLE(M)**K1 ELSE T2 = T2 + T1/DBLE(M)**K1 END IF IF ((J .LE. 0) .AND. (MOD(M,2) .NE. 0)) THEN T3 = T3 - T2/DBLE(M)**J1 ELSE T3 = T3 + T2/DBLE(M)**J1 END IF IF ((I .LE. 0) .AND. (MOD(M,2) .NE. 0)) THEN T4 = T4 - T3/DBLE(M)**I1 ELSE T4 = T4 + T3/DBLE(M)**I1 END IF 10 CONTINUE C SUM4 = T4 RETURN END DOUBLE PRECISION FUNCTION SUM5(I,J,K,L,I10,N) C --------------------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FIVEFOLD (ALTERNATING) HARMONIC SUM C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C I1 = ABS(I) J1 = ABS(J) K1 = ABS(K) L1 = ABS(L) II1= ABS(I10) C T1 = 0.0D0 T2 = 0.0D0 T3 = 0.0D0 T4 = 0.0D0 T5 = 0.0D0 C DO 10 M=1,N IF ((I10 .LE. 0) .AND. (MOD(M,2) .NE. 0)) THEN T1 = T1 - 1.0D0/DBLE(M)**II1 ELSE T1 = T1 + 1.0D0/DBLE(M)**II1 END IF IF ((L .LE. 0) .AND. (MOD(M,2) .NE. 0)) THEN T2 = T2 - T1/DBLE(M)**L1 ELSE T2 = T2 + T1/DBLE(M)**L1 END IF IF ((K .LE. 0) .AND. (MOD(M,2) .NE. 0)) THEN T3 = T3 - T2/DBLE(M)**K1 ELSE T3 = T3 + T2/DBLE(M)**K1 END IF IF ((J .LE. 0) .AND. (MOD(M,2) .NE. 0)) THEN T4 = T4 - T3/DBLE(M)**J1 ELSE T4 = T4 + T3/DBLE(M)**J1 END IF IF ((I .LE. 0) .AND. (MOD(M,2) .NE. 0)) THEN T5 = T5 - T4/DBLE(M)**I1 ELSE T5 = T5 + T4/DBLE(M)**I1 END IF 10 CONTINUE C SUM5 = T5 RETURN END DOUBLE PRECISION FUNCTION FLI3(X) C ----------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- LI3(X) FOR -1. LE . X . LE .+1 C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C A=1D0 F=0D0 AN=0D0 TCH=1D-16 1 AN=AN+1D0 A=A*X B=A/AN**3 F=F+B IF(ABS(B)-TCH)2,2,1 2 FLI3=F END DOUBLE PRECISION FUNCTION FLI4(X) C ----------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- LI4(X) FOR -1. LE . X . LE .+1 C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C A=1D0 F=0D0 AN=0D0 TCH=1D-16 1 AN=AN+1D0 A=A*X B=A/AN**4 F=F+B IF(ABS(B)-TCH)2,2,1 2 FLI4 = F END DOUBLE PRECISION FUNCTION S12(Z) C -------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- NIELSEN INTEGRAL: S12(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C EXTERNAL FINT C EPS = 1.0D-8 KEY = 2 MAX = 10000 C F = DAIND1(0.0D0,Z,FINT,EPS,KEY,MAX,KOU,EST) S12 = F/2.0D0 RETURN END DOUBLE PRECISION FUNCTION FINT(Y) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- SUBSIDIARY ROUTINE FOR THE NIELSEN INTEGRAL: S12(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C FINT = LOG(1.0D0-Y)**2/Y RETURN END DOUBLE PRECISION FUNCTION YI1(T) C -------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- I1(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /EP/EPS COMMON /KM/KEY,MAX EXTERNAL YIF C YI1 = DAIND1(0.0D0,T,YIF,EPS,KEY,MAX,KOU,EST) C RETURN END DOUBLE PRECISION FUNCTION YIF(R) C -------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- INTEGRAND OF I1(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C C YIF = LOG(1.0D0+R)*LOG(1.0D0-R)/R C RETURN END DOUBLE PRECISION FUNCTION DAIND(A,B,FUN,EPS,KEY,MAX,KOUNT,EST) C -------------------------------------------------------------- C************************************************************************ C C--- INTEGRATION ROUTINE: C CF. R. PIESSENS, ANGEW. INFORMATIK, VOL. 9 (1973) 399. C C************************************************************************ C C INPUTPARAMETERS C A,B LIMITS OF THE INTEGRATION INTERVAL C FUN FUNCTION TO BE INTEGRATED (TO BE DECLARED EXTERNAL IN THE MAIN PR.) C EPS ABSOLUTE OR RELATIVE TOLERANCE,DEPENDING OF THE VALUE OF 'KEY' C KEY =1 THEN 'EPS' DENOTES AN ABSOLUTE, =2 THEN A RELATIVE TOLERANCE C MAX UPPER BOUND ON THE NUMBERS OF INTEGRAND EVALUATIONS (MAX.LE.10000) C C OUTPUTPARAMETERS C KOUNT NUMBER OF INTEGRAND EVALUATIONS C EST ESTIMATION OF THE ABSOLUTE ERROR OF THE APPROXIMATION IMPLICIT REAL*8 (A-H,O-Z) DOUBLE PRECISION MAXIM,MINIM,MODUL1,MODUL2 INTEGER RANG(130) DIMENSION &AINIT(250),END(250),EPSIL(250),PART(250),W1(5),W2(5),W3(6), & X1(5),X2(5) DATA X1/0.973906528517D+0,0.865063366689D+0,0.679409568299D+0, * 0.433395394129D+0,0.148874338981D+0/ DATA X2/0.995657163026D+0,0.930157491356D+0,0.780817726586D+0, * 0.562757134669D+0,0.294392862701D+0/ DATA W1/0.666713443087D-1,0.149451349151D+0,0.219086362516D+0, * 0.269266719310D+0,0.295524224715D+0/ DATA W2/0.325581623080D-1,0.750396748109D-1,0.109387158802D+0, * 0.134709217311D+0,0.147739104901D+0/ DATA W3/0.116946388674D-1,0.547558965744D-1,0.931254545837D-1, * 0.123491976262D+0,0.142775938577D+0,0.149445554003D+0/ DATA TOL/0.23D-15/ EXTERNAL FUN MAX1 = (MAX+21)/42+1 MAX2 = MAX1/2+2 ALFA = A BETA = B MAAT = 1 C EVALUATION OF GAUSSIAN AND KRONROD FORMULAS 10 S = 0.5D+0*(BETA-ALFA) U = 0.5D+0*(BETA+ALFA) RES1 = 0.0D+0 RES2 = W3(6)*FUN(U) DO 20 K = 1,5 C = S*X1(K) C = FUN(C+U)+FUN(U-C) RES1 = RES1+W1(K)*C RES2 = RES2+W2(K)*C C = S*X2(K) 20 RES2 =RES2+W3(K)*(FUN(C+U)+FUN(U-C)) PAT = RES2*S MODUL2 = ABS(PAT-RES1*S) IF(MAAT.GT.1) GOTO 50 EST = MODUL2 BINT = PAT KOUNT =21 PART(1) = BINT GOTO 90 30 RANG(1) = 1 AINIT(1) = A END(1) = B EPSIL(1) = EST 40 NR = RANG(1) BINT = BINT-PART(NR) EST =EST-EPSIL(NR) C THE SUBINTERVAL WITH LARGEST ERROR IS SPLIT UP INTO TWO EQUAL PARTS ALFA = AINIT(NR) BETA = (AINIT(NR)+END(NR))*0.5 JJ = 1 MAAT = MAAT+1 GOTO 10 50 EST = EST+MODUL2 BINT = BINT+PAT IF(JJ.EQ.0) GOTO 60 MODUL1 = MODUL2 PAT1 = PAT ALFA = BETA BETA = END(NR) JJ = 0 GOTO 10 60 MA = MAAT IF(MAAT.GT.MAX2) MA = MAX1+3-MAAT IF(MODUL1.GT.MODUL2) GOTO 70 EPSIL(NR) = MODUL2 EPSIL(MAAT) = MODUL1 AINIT(MAAT) = AINIT(NR) AINIT(NR) = ALFA END(MAAT) = ALFA MAXIM = MODUL2 MINIM = MODUL1 PART(NR) = PAT PART(MAAT) = PAT1 GOTO 80 70 EPSIL(NR) = MODUL1 EPSIL(MAAT) = MODUL2 END(MAAT) = BETA END(NR) = ALFA AINIT(MAAT) = ALFA MAXIM = MODUL1 MINIM = MODUL2 PART(NR) = PAT1 PART(MAAT) = PAT 80 KOUNT = KOUNT+42 C TEST ON THE NUMBER OF FUNCTION EVALUATIONS IF(KOUNT.GE.MAX) GOTO 190 90 GOTO (100,110),KEY C TEST ON ABSOLUTE ACCURACY 100 IF(EST.LE.EPS) GOTO 190 GOTO 120 C TEST ON RELATIVE ACCURACY 110 IF(ABS(EPS*BINT).LE.TOL) GOTO 100 IF(EST.LE.ABS(EPS*BINT)) GOTO 190 120 IF(MAAT.EQ.1) GOTO 30 IF(MAAT.GT.2) GOTO 130 RANG(2) = 2 GOTO 40 130 MB = MA-1 C SEARCH FOR THE SUBINTERVAL WITH LARGEST ERROR DO 140 I = 2,MB IR = RANG(I) IF(MAXIM.GE.EPSIL(IR)) GOTO 150 140 RANG(I-1) = RANG(I) RANG(MB) = NR RANG(MA) = MAAT GOTO 40 150 RANG(I-1) = NR DO 160 K = I,MB IR = RANG(K) IF(MINIM.GE.EPSIL(IR)) GOTO 170 160 CONTINUE RANG(MA) = MAAT GOTO 40 170 DO 180 I = K,MB KK = MB-I+K 180 RANG(KK+1) = RANG(KK) RANG(K) = MAAT GOTO 40 C CALCULATION OF THE INTEGRAL 190 AIND1 = 0.0D+0 DO 200 K = 1,MAAT 200 AIND1 = AIND1+PART(K) IF(AIND1.EQ.0.0D+0) & WRITE(6,*) '**** AIND=0.**** EST NOT CALCULATED' IF(AIND1.NE.0.0D+0) EST=EST/AIND1 DAIND=AIND1 RETURN END DOUBLE PRECISION FUNCTION DAIND1(A,B,FUN,EPS,KEY,MAX,KOUNT,EST) C -------------------------------------------------------------- C************************************************************************ C C--- INTEGRATION ROUTINE: C CF. R. PIESSENS, ANGEW. INFORMATIK, VOL. 9 (1973) 399. C C************************************************************************ C INPUTPARAMETERS C A,B LIMITS OF THE INTEGRATION INTERVAL C FUN FUNCTION TO BE INTEGRATED (TO BE DECLARED EXTERNAL IN THE MAIN PR.) C EPS ABSOLUTE OR RELATIVE TOLERANCE,DEPENDING OF THE VALUE OF 'KEY' C KEY =1 THEN 'EPS' DENOTES AN ABSOLUTE, =2 THEN A RELATIVE TOLERANCE C MAX UPPER BOUND ON THE NUMBERS OF INTEGRAND EVALUATIONS (MAX.LE.10000) C C OUTPUTPARAMETERS C KOUNT NUMBER OF INTEGRAND EVALUATIONS C EST ESTIMATION OF THE ABSOLUTE ERROR OF THE APPROXIMATION IMPLICIT REAL*8 (A-H,O-Z) DOUBLE PRECISION MAXIM,MINIM,MODUL1,MODUL2 INTEGER RANG(130) DIMENSION &AINIT(250),END(250),EPSIL(250),PART(250),W1(5),W2(5),W3(6), & X1(5),X2(5) DATA X1/0.973906528517D+0,0.865063366689D+0,0.679409568299D+0, * 0.433395394129D+0,0.148874338981D+0/ DATA X2/0.995657163026D+0,0.930157491356D+0,0.780817726586D+0, * 0.562757134669D+0,0.294392862701D+0/ DATA W1/0.666713443087D-1,0.149451349151D+0,0.219086362516D+0, * 0.269266719310D+0,0.295524224715D+0/ DATA W2/0.325581623080D-1,0.750396748109D-1,0.109387158802D+0, * 0.134709217311D+0,0.147739104901D+0/ DATA W3/0.116946388674D-1,0.547558965744D-1,0.931254545837D-1, * 0.123491976262D+0,0.142775938577D+0,0.149445554003D+0/ DATA TOL/0.23D-15/ EXTERNAL FUN MAX1 = (MAX+21)/42+1 MAX2 = MAX1/2+2 ALFA = A BETA = B MAAT = 1 C EVALUATION OF GAUSSIAN AND KRONROD FORMULAS 10 S = 0.5D+0*(BETA-ALFA) U = 0.5D+0*(BETA+ALFA) RES1 = 0.0D+0 RES2 = W3(6)*FUN(U) DO 20 K = 1,5 C = S*X1(K) C = FUN(C+U)+FUN(U-C) RES1 = RES1+W1(K)*C RES2 = RES2+W2(K)*C C = S*X2(K) 20 RES2 =RES2+W3(K)*(FUN(C+U)+FUN(U-C)) PAT = RES2*S MODUL2 = ABS(PAT-RES1*S) IF(MAAT.GT.1) GOTO 50 EST = MODUL2 BINT = PAT KOUNT =21 PART(1) = BINT GOTO 90 30 RANG(1) = 1 AINIT(1) = A END(1) = B EPSIL(1) = EST 40 NR = RANG(1) BINT = BINT-PART(NR) EST =EST-EPSIL(NR) C THE SUBINTERVAL WITH LARGEST ERROR IS SPLIT UP INTO TWO EQUAL PARTS ALFA = AINIT(NR) BETA = (AINIT(NR)+END(NR))*0.5 JJ = 1 MAAT = MAAT+1 GOTO 10 50 EST = EST+MODUL2 BINT = BINT+PAT IF(JJ.EQ.0) GOTO 60 MODUL1 = MODUL2 PAT1 = PAT ALFA = BETA BETA = END(NR) JJ = 0 GOTO 10 60 MA = MAAT IF(MAAT.GT.MAX2) MA = MAX1+3-MAAT IF(MODUL1.GT.MODUL2) GOTO 70 EPSIL(NR) = MODUL2 EPSIL(MAAT) = MODUL1 AINIT(MAAT) = AINIT(NR) AINIT(NR) = ALFA END(MAAT) = ALFA MAXIM = MODUL2 MINIM = MODUL1 PART(NR) = PAT PART(MAAT) = PAT1 GOTO 80 70 EPSIL(NR) = MODUL1 EPSIL(MAAT) = MODUL2 END(MAAT) = BETA END(NR) = ALFA AINIT(MAAT) = ALFA MAXIM = MODUL1 MINIM = MODUL2 PART(NR) = PAT1 PART(MAAT) = PAT 80 KOUNT = KOUNT+42 C TEST ON THE NUMBER OF FUNCTION EVALUATIONS IF(KOUNT.GE.MAX) GOTO 190 90 GOTO (100,110),KEY C TEST ON ABSOLUTE ACCURACY 100 IF(EST.LE.EPS) GOTO 190 GOTO 120 C TEST ON RELATIVE ACCURACY 110 IF(ABS(EPS*BINT).LE.TOL) GOTO 100 IF(EST.LE.ABS(EPS*BINT)) GOTO 190 120 IF(MAAT.EQ.1) GOTO 30 IF(MAAT.GT.2) GOTO 130 RANG(2) = 2 GOTO 40 130 MB = MA-1 C SEARCH FOR THE SUBINTERVAL WITH LARGEST ERROR DO 140 I = 2,MB IR = RANG(I) IF(MAXIM.GE.EPSIL(IR)) GOTO 150 140 RANG(I-1) = RANG(I) RANG(MB) = NR RANG(MA) = MAAT GOTO 40 150 RANG(I-1) = NR DO 160 K = I,MB IR = RANG(K) IF(MINIM.GE.EPSIL(IR)) GOTO 170 160 CONTINUE RANG(MA) = MAAT GOTO 40 170 DO 180 I = K,MB KK = MB-I+K 180 RANG(KK+1) = RANG(KK) RANG(K) = MAAT GOTO 40 C CALCULATION OF THE INTEGRAL 190 AIND1 = 0.0D+0 DO 200 K = 1,MAAT 200 AIND1 = AIND1+PART(K) IF(AIND1.EQ.0.0D+0) & WRITE(6,*) '**** AIND=0.**** EST NOT CALCULATED' IF(AIND1.NE.0.0D+0) EST=EST/AIND1 DAIND1=AIND1 RETURN END DOUBLE PRECISION FUNCTION FCT1(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT1(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT1 C NN=N F = DAIND(0.0D0,1.0D0,FKT1,EPS,KEY,MAX,KOU,EST) C FCT1=F C RETURN END DOUBLE PRECISION FUNCTION FKT1(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1+X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = LOG(1.0D0+X)/(1.0D0+X)*X**N C FKT1=F C RETURN END DOUBLE PRECISION FUNCTION FCT2(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT2(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT2 C NN=N F = DAIND(0.0D0,1.0D0,FKT2,EPS,KEY,MAX,KOU,EST) C FCT2=F C RETURN END DOUBLE PRECISION FUNCTION FKT2(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG^2(1+X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C T = LOG(1.0D0+X) F = T**2*X**N/(1.0D0+X) C FKT2=F C RETURN END DOUBLE PRECISION FUNCTION FCT3(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT3(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT3 C NN=N F = DAIND(0.0D0,1.0D0,FKT3,EPS,KEY,MAX,KOU,EST) C FCT3=F C RETURN END DOUBLE PRECISION FUNCTION FKT3(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI2(X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = FLI2(X)/(1.0D0+X)*X**(N) C FKT3=F C RETURN END DOUBLE PRECISION FUNCTION FCT4(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT4(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT4 C NN=N F = DAIND(0.0D0,1.0D0,FKT4,EPS,KEY,MAX,KOU,EST) C FCT4=F C RETURN END DOUBLE PRECISION FUNCTION FKT4(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI2(-X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = FLI2(-X)/(1.0D0+X)*X**(N) C FKT4=F C RETURN END DOUBLE PRECISION FUNCTION FCT5(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT5(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT5 C NN=N F = DAIND(0.0D0,1.0D0,FKT5,EPS,KEY,MAX,KOU,EST) C FCT5=F C RETURN END DOUBLE PRECISION FUNCTION FKT5(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(X)*LI2(X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = LOG(X)*FLI2(X)/(1.0D0+X)*X**(N) C FKT5=F C RETURN END DOUBLE PRECISION FUNCTION FCT6(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT6(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT6 C NN=N F = DAIND(0.0D0,1.0D0,FKT6,EPS,KEY,MAX,KOU,EST) C FCT6=F C RETURN END DOUBLE PRECISION FUNCTION FKT6(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI3(X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = FLI3(X)/(1.0D0+X)*X**(N) C FKT6=F C RETURN END DOUBLE PRECISION FUNCTION FCT7(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT7(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT7 C NN=N F = DAIND(0.0D0,1.0D0,FKT7,EPS,KEY,MAX,KOU,EST) C FCT7=F C RETURN END DOUBLE PRECISION FUNCTION FKT7(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI3(-X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = FLI3(-X)/(1.0D0+X)*X**(N) C FKT7=F C RETURN END DOUBLE PRECISION FUNCTION FCT8(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT8(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT8 C NN=N F = DAIND(0.0D0,1.0D0,FKT8,EPS,KEY,MAX,KOU,EST) C FCT8=F C RETURN END DOUBLE PRECISION FUNCTION FKT8(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: S12(X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = S12(X)/(1.0D0+X)*X**(N) C FKT8=F C RETURN END DOUBLE PRECISION FUNCTION FCT9(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT9(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT9 C NN=N F = DAIND(0.0D0,1.0D0,FKT9,EPS,KEY,MAX,KOU,EST) C FCT9=F C RETURN END DOUBLE PRECISION FUNCTION FKT9(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: S12(-X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = S12(-X)/(1.0D0+X)*X**(N) C FKT9=F C RETURN END DOUBLE PRECISION FUNCTION FCT10(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT10(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT10 C NN=N F = DAIND(0.0D0,1.0D0,FKT10,EPS,KEY,MAX,KOU,EST) C FCT10=F C RETURN END DOUBLE PRECISION FUNCTION FKT10(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: I1(X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N EXTERNAL YI1 C C T1=X**N F = YI1(X)*T1/(1.0D0+X) C FKT10=F C RETURN END DOUBLE PRECISION FUNCTION FCT11(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT11(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT11 C NN=N F = DAIND(0.0D0,1.0D0,FKT11,EPS,KEY,MAX,KOU,EST) C FCT11=F C RETURN END DOUBLE PRECISION FUNCTION FKT11(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1-X)*LI2(X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = LOG(1.0D0-X)*FLI2(X)/(1.0D0+X)*X**(N) C FKT11=F C RETURN END DOUBLE PRECISION FUNCTION FCT12(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT12(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT12 C NN=N F = DAIND(0.0D0,1.0D0,FKT12,EPS,KEY,MAX,KOU,EST) C FCT12=F C RETURN END DOUBLE PRECISION FUNCTION FKT12(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1-X)*LI2(-X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C X2=X**2 F = LOG(1.0D0-X)*FLI2(-X)/(1.0D0+X)*X**(N) C FKT12=F C RETURN END DOUBLE PRECISION FUNCTION FCT13(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT13(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT13 C NN=N F = DAIND(0.0D0,1.0D0,FKT13,EPS,KEY,MAX,KOU,EST) C FCT13=F C RETURN END DOUBLE PRECISION FUNCTION FKT13(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1+X)*LI2(-X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C F = LOG(1.0D0+X)*FLI2(-X)/(1.0D0+X)*X**(N) C FKT13=F C RETURN END DOUBLE PRECISION FUNCTION FCT14(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT14(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT14 C NN=N F = DAIND(0.0D0,1.0D0,FKT14,EPS,KEY,MAX,KOU,EST) C FCT14=F C RETURN END DOUBLE PRECISION FUNCTION FKT14(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LOG^2(1+X)-LOG^2(2))/(X-1) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C T = LOG(1.0D0+X) F = (T**2 -D2**2)/(X-1.0D0)*X**(N) C FKT14=F C RETURN END DOUBLE PRECISION FUNCTION FCT15(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT15(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT15 C NN=N F = DAIND(0.0D0,1.0D0,FKT15,EPS,KEY,MAX,KOU,EST) C FCT15=F C RETURN END DOUBLE PRECISION FUNCTION FKT15(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LOG(1+X)-LOG(2))/(X-1)*LI2(X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = (LOG(1.0D0+X)-D2)/(X-1.0D0)*FLI2(X)*X**(N) C FKT15=F C RETURN END DOUBLE PRECISION FUNCTION FCT16(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT16(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT16 C NN=N F = DAIND(0.0D0,1.0D0,FKT16,EPS,KEY,MAX,KOU,EST) C FCT16=F C RETURN END DOUBLE PRECISION FUNCTION FKT16(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LOG(1+X)-LOG(2))/(X-1)*LI2(-X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = (LOG(1.0D0+X)-D2)/(X-1.0D0)*X**(N)*FLI2(-X) C FKT16=F C RETURN END DOUBLE PRECISION FUNCTION FCT17(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT17(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT17 C NN=N F = DAIND(0.0D0,1.0D0,FKT17,EPS,KEY,MAX,KOU,EST) C FCT17=F C RETURN END DOUBLE PRECISION FUNCTION FKT17(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(X)*LOG^2(1+X)/(X-1) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C T = LOG(1.0D0+X) F = LOG(X)* T**2*(X**N )/(X-1.0D0) C FKT17=F C RETURN END DOUBLE PRECISION FUNCTION FCT18(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT18(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT18 C NN=N F = DAIND(0.0D0,0.99999999999999D0,FKT18,EPS,KEY,MAX,KOU,EST) C FCT18=F C RETURN END DOUBLE PRECISION FUNCTION FKT18(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI2(X)-ZETA2)/(X-1) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = (FLI2(X)-ZETA2)/(X-1.0D0)*X**N C FKT18=F C RETURN END DOUBLE PRECISION FUNCTION FCT19(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT19(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT19 C NN=N F = DAIND(0.0D0,1.0D0,FKT19,EPS,KEY,MAX,KOU,EST) C FCT19=F C RETURN END DOUBLE PRECISION FUNCTION FKT19(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI2(-X)+ZETA2/2)/(X-1) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = (FLI2(-X)+ZETA2/2.0D0)/(X-1.0D0)*X**N C FKT19=F C RETURN END DOUBLE PRECISION FUNCTION FCT20(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT20(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT20 C NN=N F = DAIND(0.0D0,1.0D0,FKT20,EPS,KEY,MAX,KOU,EST) C FCT20=F C RETURN END DOUBLE PRECISION FUNCTION FKT20(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI3(X)-ZETA3)/(X-1) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = (FLI3(X)-ZETA3)/(X-1.0D0)*X**N C FKT20=F C RETURN END DOUBLE PRECISION FUNCTION FCT21(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT21(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT21 C NN=N F = DAIND(0.0D0,0.99999999999D0,FKT21,EPS,KEY,MAX,KOU,EST) C FCT21=F C RETURN END DOUBLE PRECISION FUNCTION FKT21(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (S12(X)-ZETA3)/(X-1) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = (S12(X)-ZETA3)/(X-1.0D0)*X**N C FKT21=F C RETURN END DOUBLE PRECISION FUNCTION FCT22(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT22(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT22 C NN=N F = DAIND(0.0D0,1.0D0,FKT22,EPS,KEY,MAX,KOU,EST) C FCT22=F C RETURN END DOUBLE PRECISION FUNCTION FKT22(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(X)*LI2(X)/(X-1) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = LOG(X)*FLI2(X)/(X-1.0D0)*X**N C FKT22=F C RETURN END DOUBLE PRECISION FUNCTION FCT23(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT23(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT23 C NN=N F = DAIND(0.0D0,1.0D0,FKT23,EPS,KEY,MAX,KOU,EST) C FCT23=F C RETURN END DOUBLE PRECISION FUNCTION FKT23(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI3(-X)+3/4*ZETA2)/(X-1) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = (FLI3(-X)+3.0D0/4.0D0*ZETA3)/(X-1.0D0)*X**N C FKT23=F C RETURN END DOUBLE PRECISION FUNCTION FCT24(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT24(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT24 C NN=N F = DAIND(0.0D0,1.0D0,FKT24,EPS,KEY,MAX,KOU,EST) C FCT24=F C RETURN END DOUBLE PRECISION FUNCTION FKT24(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (I1(X)+5/8*ZETA3)/(X-1) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C F = (YI1(X)+5.0D0/8.0D0*ZETA3)/(X-1)*X**N C FKT24=F C RETURN END DOUBLE PRECISION FUNCTION FCT25(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT25(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT25 C NN=N F = DAIND(0.0D0,1.0D0,FKT25,EPS,KEY,MAX,KOU,EST) C FCT25=F C RETURN END DOUBLE PRECISION FUNCTION FKT25(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (S12(X)-ZETA3)/(X-1) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C C F = (S12(-X)-ZETA3/8.0D0)/(X-1.0D0)*X**N C FKT25=F C RETURN END DOUBLE PRECISION FUNCTION FCT26(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN MOMENT FOR POSITIVE INTEGER ARGUMENT OF FKT25(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ NN C EXTERNAL FKT26 C NN=N F = DAIND(0.0D0,1.0D0,FKT26,EPS,KEY,MAX,KOU,EST) C FCT26=F C RETURN END DOUBLE PRECISION FUNCTION FKT26(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG^3(1-X)/(1+X) C--- INTEGRAND FOR C--- NUMERICAL INTEGRAL FOR POSITIVE INTEGER N C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 COMMON /EP/EPS COMMON /KM/KEY,MAX COMMON/EXPO/ N C F=(LOG(1.0D0-X))**3/(1.0D0+X)*X**N C FKT26=F C RETURN END DOUBLE PRECISION FUNCTION XCG1(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1+X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 N1=N C IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF C T1=SUM2(-1,1,N1) T2=SUM1(1,N1) T3=SUM1(-1,N1) T4=SUM1(-2,N1) C T=(DL*DL/2.0D0+T1-(T2-T3)*DL-T2*T3-T4)*IFA C XCG1=T C RETURN END DOUBLE PRECISION FUNCTION XCG2(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG^2(1+X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF T1=SUM3(1,1,-1,N1) T2=SUM2(1,-1,N1) T3=SUM2(1,1,N1) T4=SUM1(1,N1) T5=SUM1(-1,N1) C T=(T1-DL*(T2-T3)-DL**2/2.0D0*(T4-T5)+DL**3/6.0D0)*IFA*2.0D0 C XCG2=T C RETURN END DOUBLE PRECISION FUNCTION XCG3(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI2(X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF T1=SUM2(-2,1,N1) T2=SUM1(-1,N1) C IFA=-IFA T= (T1-ZETA2*T2+5.0D0/8.0D0*ZETA3-ZETA2*DL)*IFA C XCG3=T C RETURN END DOUBLE PRECISION FUNCTION XCG4(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI2(-X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF T1=SUM2(2,-1,N1) T2=SUM1(-1,N1) T3=SUM1(2,N1) T4=SUM1(-2,N1) C IFA=-IFA T= (T1+DL*(T3-T4)+ZETA2*T2/2.0D0-ZETA3/4.0D0+ZETA2*DL/2.0D0)*IFA C XCG4=T C RETURN END DOUBLE PRECISION FUNCTION XCG5(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(X)*LI2(X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF T0=SUM2(-2,2,N1) T1=SUM2(-3,1,N1) T2=SUM1(-2,N1) T=(T0+2.0D0*T1-2.0D0*ZETA2*T2-ZETA2**2*3.0D0/40.0D0)*IFA C XCG5=T C RETURN END DOUBLE PRECISION FUNCTION XCG6(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI3(X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF T1=SUM2(-3,1,N1) T2=SUM1(-2,N1) T3=SUM1(-1,N1) C T=(T1-ZETA2*T2+ZETA3*T3+3.0D0/5.0D0*ZETA2**2-2.0D0*XLI4 & -3.0D0/4.0D0*ZETA3*DL+ZETA2*DL**2/2.0D0-DL**4/12.0D0)*IFA C XCG6=T C RETURN END DOUBLE PRECISION FUNCTION XCG7(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LI3(-X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF T1=SUM2(3,-1,N1) T2=SUM1(3,N1) T3=SUM1(-3,N1) T4=SUM1(-2,N1) T5=SUM1(-1,N1) C T=(T1+DL*(T2-T3)+ZETA2/2.0D0*T4-3.0D0/4.0D0*ZETA3*T5 & +ZETA2**2/8.0D0 & -3.0D0/4.0D0*ZETA3*DL)*IFA C XCG7=T C RETURN END DOUBLE PRECISION FUNCTION XCG8(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: S12(X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF T1=SUM3(-2,1,1,N1) T2=SUM1(-1,N1) C T=-IFA*(T1+XLI4-ZETA3*T2-ZETA2**2/8.0D0-ZETA3*DL/8.0D0 & -ZETA2*DL**2/4.0D0+DL**4/24.0D0) C XCG8=T C RETURN END DOUBLE PRECISION FUNCTION XCG9(N) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: S12(-X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 C N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF T1=SUM3(2,1,-1,N1) T2=SUM2(2,1,N1) T3=SUM2(2,-1,N1) T4=SUM1(2,N1) T5=SUM1(-2,N1) T6=SUM1(-1,N1) C T=-(T1+DL*(T2-T3)-DL*DL/2.0D0*(T4-T5)-ZETA3/8.0D0*T6-3.0D0*XLI4 & +6.0D0/5.0D0*ZETA2**2-11.0D0/4.0D0*ZETA3*DL & +3.0D0/4.0D0*ZETA2*DL*DL-DL**4/8.0D0)*IFA C IFA=-IFA XCG9=T C RETURN END DOUBLE PRECISION FUNCTION XCG10(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: I1(X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 C N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF C T1=SUM3(-2,-1,-1,N1) T2=SUM3(2,-1,1,N1) T3=SUM2(-2,1,N1) T4=SUM2(-2,-1,N1) T5=SUM1(2,N1) T6=SUM1(-2,N1) T7=SUM1(-1,N1) C T= -(T1+T2-DL*(T3-T4)+(T5-T6)/2.0D0*(ZETA2-DL**2) & +5.0D0/8.0D0*ZETA3*(T7+DL)-3.0D0/20.0D0*ZETA2**2)*IFA C IFA=-IFA XCG10=T C RETURN END DOUBLE PRECISION FUNCTION XCG11(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1-X)*LI2(X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 C N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF T1=SUM3(-1,2,1,N1) T2=SUM2(-1,1,N1) T3=SUM3(-2,1,1,N1) T4=SUM1(-1,N1) C S12R=-IFA*(T3+XLI4-ZETA3*T4-ZETA2**2/8.0D0-ZETA3*DL/8.0D0 & -ZETA2*DL**2/4.0D0+DL**4/24.0D0) C T=(T1-ZETA2*T2-19.0D0/40.0D0*ZETA2**2+XLI4+ZETA3*DL/4.0D0 & +DL**2*ZETA2/4.0D0+DL**4/24.0D0)*IFA-2.0D0*S12R C XCG11=T C RETURN END DOUBLE PRECISION FUNCTION XCG12(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1-X)*LI2(-X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 C N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF C T1=SUM3(2,-1,1,N1) T2=SUM3(-2,-1,-1,N1) T3=SUM3(-1,-2,-1,N1) T4=SUM2(-2, 1,N1) T5=SUM2(-1,2,N1) T6=SUM2(-1,1,N1) T7=SUM1(-1,N1) T8=SUM1(-2,N1) T9=SUM1(3,N1) T10=SUM1(2,N1) T11=SUM1(-1,N1) C T=(T1+T2+T3-(T4+T5)*DL+T6*ZETA2/2.0D0+T7*T8*DL+T9*DL &+(ZETA2-DL**2)/2.0D0*(T10-T8)+5.0D0/8.0D0*ZETA3*T7-4.0D0*XLI4 &+3.0D0/2.0D0*ZETA2**2-21.0D0/8.0D0*ZETA3*DL &+3.0D0/4.0D0*ZETA2*DL**2-DL**4/6.0D0)*IFA C XCG12=T C RETURN END DOUBLE PRECISION FUNCTION XCG13(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(1+X)*LI2(-X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 N1=N IF(MOD(N1,2).NE.1) THEN IFA= 1 ELSE IFA=-1 ENDIF C T1=SUM3(1,2,-1,N1) T2=SUM3(2,1,-1,N1) T3=SUM2(2,1,N1) T4=SUM2(1,-2,N1) T5=SUM2(2,-1,N1) T6=SUM1(1,N1) T7=SUM1(2,N1) T8=SUM1(3,N1) T9=SUM1(-1,N1) T10=SUM2(1,-1,N1) T11=SUM1(-2,N1) T12=SUM1(1 ,N1) C T=(T1+2.0D0*T2+(T3-T4-2*T5+T6*T7+T8-ZETA2/2.0D0*T9)*DL & +T10*ZETA2/2.0D0-(T7-T11)*DL**2 & -(ZETA3/4.0D0-ZETA2*DL/2.0D0)*T12 & -3.0D0*XLI4+6.0D0/5.0D0*ZETA2**2-21.0D0/8.0D0*ZETA3*DL & +ZETA2/2.0D0*DL**2-DL**4/8.0D0)*IFA C XCG13=T C RETURN END DOUBLE PRECISION FUNCTION XCG14(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LOG^2(1+X)-LOG^2(2))/(X-1) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 N1=N C T1=SUM3(-1,1,-1,N1) T2=SUM2(-1,-1,N1) T3=SUM2(-1,1,N1) T4=SUM1(1,N1) T5=SUM1(-1,N1) C T=(T1-DL*(T2-T3)+DL*DL/2.0D0*(T4-T5))*2.0D0 T=T-DL**2*T4-ZETA3/4.0D0+ZETA2*DL-2.0D0/3.0D0*DL**3 C XCG14=T C RETURN END DOUBLE PRECISION FUNCTION XCG15(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LOG(1+X)-LOG(2))/(X-1)*LI2(X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 N1=N C T1=SUM3(-1,-2,1,N1) T2=SUM3(2,-1,-1,N1) T3=SUM3(-2,-1,1,N1) T4=SUM2(-1,-1,N1) T5=SUM1(1,N1) T6=SUM1(-1,N1) T7=SUM2(2,1,N1) T8=SUM2(2,-1,N1) T9=SUM1(2,N1) T10=SUM1(-2,N1) C T=T1+T2+T3-ZETA2*T4-(5.0D0/8.0D0*ZETA3-ZETA2*DL)*(T5-T6) & +5.0D0/8.0D0*ZETA3*T5-DL*(T7-T8) & -(ZETA2-DL**2)/2.0D0*(T9-T10) C >> & -DL*( ZETA2*T5) & +19.0D0/40.0D0*ZETA2**2-XLI4+7.0D0/4.0D0*ZETA3*DL & -ZETA2*DL**2/4.0D0-DL**4/24.0D0 & +DL*(SUM2(2,1,N1)-ZETA3*2.0D0) C XCG15=T C RETURN END DOUBLE PRECISION FUNCTION XCG16(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LOG(1+x)-LOG(2))/(X-1)*LI2(-X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 N1=N C T= 2.0D0*SUM3(-2,1,-1,N)+SUM3(-1,2,-1,N) & +DL*(2.0D0*(-SUM2(-2,-1,N)+SUM2(-2,1,N)) & -SUM2(-1,-2,N)+SUM2(-1,2,N)) & +ZETA2/2.0D0*SUM2(-1,-1,N)-DL**2*(SUM1(-2,N)-SUM1(2,N)) & -ZETA3/4.0D0*SUM1(1,N) & -(ZETA3/4.0D0-ZETA2*DL/2.0D0)*(SUM1(-1,N)-SUM1(1,N)) C>> & +DL*(SUM2(-2,-1,N)-DL*(SUM1(2,N)-SUM1(-2,N)) & +ZETA2/2.0D0*SUM1(1,N)) & -33.0D0/20.0D0*ZETA2**2+4.0D0*XLI4 & +13.0D0/4.0D0*ZETA3*DL-3.0D0/4.0D0*ZETA2*DL**2+DL**4/6.0D0 C XCG16=T C RETURN END DOUBLE PRECISION FUNCTION XCG17(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(X)*LOG^2(1+X)/(X-1) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C N1=N DL=D2 XLI4=ZLI4 C T1= SUM2(-1,-2,N) " T2= SUM2(-1, 2,N) T3= SUM2(-1,-1,N) T4= SUM2(-1, 1,N) T5= SUM1(-1,N) T6= SUM1( 1,N) T7= SUM2(-2, 1,N) T8= SUM2(-2,-1,N) T9= SUM1(-2, N) T10=SUM1( 2, N) C U1=DL*(T1-T2)+(ZETA3/8.0D0)*(T5-T6) U2=-ZETA2/2.0D0*T4 U3=-(T7-T8)*DL+(T9-T10)*DL**2/2.0D0 +ZETA3/8.0D0*T6 C TEST1B=2.0D0*(SUM3(-1,2,-1,N)+SUM3(-1,1,-2,N)+SUM3(-2,1,-1,N)) T = (U1+U2+U3)*2.0D0-TEST1B CO = 7.0D0/4.0D0*ZETA2**2-4.0D0*ZLI4-21.0D0/4.0D0*ZETA3*D2 & +5.0D0/2.0D0*ZETA2*D2**2-D2**4/6.0D0 C XCG17= T+CO RETURN END DOUBLE PRECISION FUNCTION XCG18(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI2(X)-ZETA2)/(X-1) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C N1=N DL=D2 XLI4=ZLI4 C N1=N C T1=SUM2(2,1,N1) C T=-T1+2.0D0*ZETA3 C XCG18= T C RETURN END DOUBLE PRECISION FUNCTION XCG19(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI2(-X)+ZETA2/2)/(X-1) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C N1=N DL=D2 XLI4=ZLI4 C T1=SUM2(-2,-1,N1) T2=SUM1(2,N1) T3=SUM1(-2,N1) T4=SUM1(1,N1) C T=-T1+DL*(T2-T3)-5.0D0/8.0D0*ZETA3 C XCG19= T C RETURN END DOUBLE PRECISION FUNCTION XCG20(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI3(X)-ZETA3)/(X-1) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C N1=N DL=D2 XLI4=ZLI4 C T1=SUM1(1,N1) T2=SUM1(2,N1) T3=SUM2(3,1,N1) C T= -ZETA2*T2+T3+ZETA2**2/2.0D0 C XCG20= T C RETURN END DOUBLE PRECISION FUNCTION XCG21(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (S12(X)-ZETA3)/(X-1) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C N1=N DL=D2 XLI4=ZLI4 C T1=SUM3(2,1,1,N1) T2=SUM1(1,N1) C T=-T1+6.0D0/5.0D0*ZETA2**2 C XCG21= T C RETURN END DOUBLE PRECISION FUNCTION XCG22(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG(X)*LI2(X)/(X-1) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 C N1=N C T1=SUM1(2,N1) T2=SUM1(4,N1) T3=SUM2(3,1,N1) C T=-2.0D0*ZETA2*T1+T1**2/2.0D0+T2/2.0D0+2.0D0*T3 & +3.0D0/10.0D0*ZETA2**2 C XCG22=T C RETURN END DOUBLE PRECISION FUNCTION XCG23(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (LI3(-X)+3*ZETA3/4)/(X-1) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 C N1=N C T1=SUM2(-3,-1,N1) T2=SUM1(3,N1) T3=SUM1(-3,N1) T4=SUM1(2,N1) T5=SUM1(1,N1) C T= T1-(T2-T3)*DL+ZETA2/2.0D0*T4-3.0D0/4.0D0*ZETA3*T5 & +2.0D0*XLI4-11.0D0/10.0D0*ZETA2**2+7.0D0/4.0D0*ZETA3*DL & -ZETA2/2.0D0*DL**2+DL**4/12.0D0+3.0D0/4.0D0*ZETA3*T5 C XCG23= T C RETURN END DOUBLE PRECISION FUNCTION XCG24(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (I1(X)+5/8*ZETA3)/(X-1) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 N1=N C T1=SUM3(2,-1,-1,N1) T2=SUM3(-2,-1, 1,N1) T3=SUM2(2, 1, N1) T4=SUM2(2,-1, N1) T5=SUM1(2,N1) T6=SUM1(-2,N1) T7=SUM1(1,N1) C T= C -5.0D0/8.0D0*ZETA3*T7 & -T1-T2+DL*(T3-T4)+(ZETA2-DL**2)/2.0D0*(T5-T6) & +ZETA2**2/4.0D0-2.0D0*XLI4-7.0D0/4.0D0*ZETA3*DL & +ZETA2*DL**2/2.0D0 -DL**4/12.0D0 C XCG24=T C RETURN END DOUBLE PRECISION FUNCTION XCG25(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: (S12(-X)-ZETA(3)/8)/(X-1) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 C N1=N C T1=SUM3(-2,1,-1,N1) T2=SUM2(-2,1,N1) T3=SUM2(-2,-1,N1) T4=SUM1(-2,N1) T5=SUM1(2,N1) T6=SUM1(1,N1) C T= -T1-(T2-T3)*DL+(T4-T5)*DL**2/2.0D0+3.0D0/40.0D0*ZETA2**2 C XCG25=T C RETURN END DOUBLE PRECISION FUNCTION XCG26(N) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- MELLIN TRANSFORM FOR: LOG^3(1-X)/(1+X) C--- SUM REPRESENTATION FOR INTEGER N C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C COMMON /PIZ/PI,ZETA2,ZETA3,ZLI4,D2 C DL=D2 XLI4=ZLI4 C T1=SUM4(-1,1,1,1,N) IF(MOD(N,2).EQ.1) IFA=1 IF(MOD(N,2).EQ.0) IFA=-1 C T=(T1+XLI4)*6*IFA C XCG26=T C RETURN END DOUBLE PRECISION FUNCTION FKN1(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LOG(1+X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = LOG(1.0D0+X)/(1.0D0+X) C FKN1=F C RETURN END DOUBLE PRECISION FUNCTION FKN2(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LOG^2(1+X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C C T = LOG(1.0D0+X) F = T**2/(1.0D0+X) C FKN2=F C RETURN END DOUBLE PRECISION FUNCTION FKN3(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LI2(X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = FLI2(X)/(1.0D0+X) C FKN3=F C RETURN END DOUBLE PRECISION FUNCTION FKN4(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LI2(-X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C C F = FLI2(-X)/(1.0D0+X) C FKN4=F C RETURN END DOUBLE PRECISION FUNCTION FKN5(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LOG(X)*LI2(X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = LOG(X)*FLI2(X)/(1.0D0+X) C FKN5=F C RETURN END DOUBLE PRECISION FUNCTION FKN6(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LI3(X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = FLI3(X)/(1.0D0+X) C FKN6=F C RETURN END DOUBLE PRECISION FUNCTION FKN7(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LI3(-X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = FLI3(-X)/(1.0D0+X) C FKN7=F C RETURN END DOUBLE PRECISION FUNCTION FKN8(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION S12(X))/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = S12(X)/(1.0D0+X) C FKN8=F C RETURN END DOUBLE PRECISION FUNCTION FKN9(X) C --------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION S12(-X))/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = S12(-X)/(1.0D0+X) C FKN9=F C RETURN END DOUBLE PRECISION FUNCTION FKN10(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION I1(X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C EXTERNAL YI1 C F = YI1(X)/(1.0D0+X) C FKN10=F C RETURN END DOUBLE PRECISION FUNCTION FKN11(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LOG(1-X)*LI2(X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = LOG(1.0D0-X)*FLI2(X)/(1.0D0+X) C FKN11=F C RETURN END DOUBLE PRECISION FUNCTION FKN12(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LOG(1-X)*LI2(-X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = LOG(1.0D0-X)*FLI2(-X)/(1.0D0+X) C FKN12=F C RETURN END DOUBLE PRECISION FUNCTION FKN13(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LOG(1+X)*LI2(-X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = LOG(1.0D0+X)*FLI2(-X)/(1.0D0+X) C FKN13=F C RETURN END DOUBLE PRECISION FUNCTION FKN14(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION (LOG^2(1+X)-LOG^2(2))/(X-1) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C T = LOG(1.0D0+X) F = (T**2 -(LOG(2.0D0))**2)/(X-1.0D0) C FKN14=F C RETURN END DOUBLE PRECISION FUNCTION FKN15(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION (LOG(1+X)-LOG(2))/(X-1)*LI2(X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = (LOG(1.0D0+X)-LOG(2.0D0))/(X-1.0D0)*FLI2(X) C FKN15=F C RETURN END DOUBLE PRECISION FUNCTION FKN16(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION (LOG(1+X)-LOG(2))/(X-1)*LI2(-X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = (LOG(1.0D0+X)-LOG(2.0D0))/(X-1.0D0)*FLI2(-X) C FKN16=F C RETURN END DOUBLE PRECISION FUNCTION FKN17(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LOG(X)*LOG^2(1+X)/(X-1) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C T = LOG(1.0D0+X) F = LOG(X)* T**2/(X-1.0D0) C FKN17=F C RETURN END DOUBLE PRECISION FUNCTION FKN18(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION (LI2(X)-ZETA2)/(X-1) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) COMMON /ZET2/ ZETA2 C F = (FLI2(X)-ZETA2)/(X-1.0D0) C FKN18=F C RETURN END DOUBLE PRECISION FUNCTION FKN19(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION (LI2(-X)+ZETA2/2)/(X-1) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) COMMON /ZET2/ ZETA2 C F = (FLI2(-X)+ZETA2/2.0D0)/(X-1.0D0) C FKN19=F C RETURN END DOUBLE PRECISION FUNCTION FKN20(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION (LI3(X)-ZETA3)/(X-1) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) COMMON /ZET3/ ZETA3 C F = (FLI3(X)-ZETA3)/(X-1.0D0) C FKN20=F C RETURN END DOUBLE PRECISION FUNCTION FKN21(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION (S12(X)-ZETA3)/(X-1) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) COMMON /ZET3/ ZETA3 C F = (S12(X)-ZETA3)/(X-1.0D0) C FKN21=F C RETURN END DOUBLE PRECISION FUNCTION FKN22(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LOG(X)*LI2(X)/(X-1) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F = LOG(X)*FLI2(X)/(X-1.0D0) C FKN22=F C RETURN END DOUBLE PRECISION FUNCTION FKN23(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION (LI3(-X)+3/4*ZETA3)/(X-1) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) COMMON /ZET3/ ZETA3 C F = (FLI3(-X)+3.0D0/4.0D0*ZETA3)/(X-1.0D0) C FKN23=F C RETURN END DOUBLE PRECISION FUNCTION FKN24(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION (I1(X)+5/8*ZETA3)/(X-1) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) COMMON /ZET3/ ZETA3 C F = (YI1(X)+5.0D0/8.0D0*ZETA3)/(X-1) C FKN24=F C RETURN END DOUBLE PRECISION FUNCTION FKN25(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION (S12(-X)-ZETA3/8)/(X-1) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) COMMON /ZET3/ ZETA3 C F = (S12(-X)-ZETA3/8.0D0)/(X-1.0D0) C FKN25=F C RETURN END DOUBLE PRECISION FUNCTION FKN26(X) C ---------------------------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- FUNCTION LOG^3(1-X)/(1+X) C C************************************************************************ C IMPLICIT REAL*8(A-H,O-Z) C F=(LOG(1.0D0-X))**3/(1.0D0+X) C FKN26=F C RETURN END SUBROUTINE UINIT C ---------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- USER INITIALIZATION OF RUNNING FLAGS C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) C C--- CHANGE THE DEFAULT VALUES OF FLAGS AND RUNNING PARAMETERS C COMMON/IAPP / IAPP COMMON/RUN / IRUN COMMON /EP/EPS COMMON/TEST/ ITEST1,ITEST2,ITEST3 COMMON/MOMPA/ NMIN,NMAX COMMON/FUNPA/ IMIN,IMAX C IRUN = 0 EPS = 1.0D-9 ITEST1=1 ITEST2=1 ITEST3=1 IAPP =1 IMIN=1 IMAX=26 NMIN=1 NMAX=20 C RETURN END SUBROUTINE URUN C ---------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- USER RUNNING: C--- HERE THE FUNCTIONS & SUBROUTINES C--- FCTi(N), ACGi(Z) and XCGi(N) may be accessed and combined C--- to other structures C C************************************************************************ C IMPLICIT REAL*8 (A-H,O-Z) COMPLEX*16 & ACG1,ACG2,ACG3,ACG4,ACG5,ACG6,ACG7,ACG8,ACG9,ACG10, & ACG11,ACG12,ACG13,ACG14,ACG15,ACG16,ACG17,ACG18,ACG19, & ACG20,ACG21,ACG22,ACG23,ACG24,ACG25,ACG26 C EXTERNAL FCT1,FCT2,FCT3,FCT4,FCT5,FCT6,FCT7,FCT8,FCT9,FCT10, & FCT11,FCT12,FCT13,FCT14,FCT15,FCT16,FCT17,FCT18,FCT19, & FCT20,FCT21,FCT22,FCT23,FCT24,FCT25,FCT26 EXTERNAL XCG1,XCG2,XCG3,XCG4,XCG5,XCG6,XCG7,XCG8,XCG9,XCG10, & XCG11,XCG12,XCG13,XCG14,XCG15,XCG16,XCG17,XCG18,XCG19, & XCG20,XCG21,XCG22,XCG23,XCG24,XCG25,XCG26 EXTERNAL ACG1,ACG2,ACG3,ACG4,ACG5,ACG6,ACG7,ACG8,ACG9,ACG10, & ACG11,ACG12,ACG13,ACG14,ACG15,ACG16,ACG17,ACG18,ACG19, & ACG20,ACG21,ACG22,ACG23,ACG24,ACG25,ACG26 C RETURN END SUBROUTINE UOUT C ---------------- C************************************************************************ C C J. BLUEMLEIN: 01.10.1999 (1.00) C C************************************************************************ C C--- USER OUTPUT C C************************************************************************ C RETURN END