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503 lines
20 KiB
503 lines
20 KiB
c ------------------------------------------------
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double complex function HPL3arm1(n1,n2,n3,x)
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implicit none
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integer n1,n2,n3,j,bcflag,s,szp
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double complex x,ris,myi,zp,llzp
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double precision pi, zeta2, zeta3,ll2,xre
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pi=3.1415926535897932385D0
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zeta3=1.20205690315959428539973816151d0
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zeta2=pi**2/6d0
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myi = dcmplx(0d0,1d0)
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ll2 = dlog(2d0)
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bcflag = 0
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j=1+(n3+1)*1+(n2+1)*3+(n1+1)*9
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ris = dcmplx(0d0,0d0)
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c--- +i*epsilon to get branch cuts right ---
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if (dimag(x).eq.0d0) then
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x = x + dcmplx(0d0,1d-60)
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bcflag = 1
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endif
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c---
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select case (j)
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c This was file contains the Taylor
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c expansions around x = -1
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c The expansion parameter is zp = x+1
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case(1) !-1-1-1
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zp = x+1d0
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llzp = log(zp)
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ris = (llzp**3)/6d0
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case(2) !-1-10
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zp = x+1d0
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llzp = log(zp)
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szp = s(zp)
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ris = -zp - (zp**2)/8d0 - (zp**3)/27d0 - (z
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&p**4)/64d0 - (zp**5)/125d0 - (zp**6)/216d0 - (zp**7)/34
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&3d0 - (zp**8)/512d0 - (zp**9)/729d0 + (pi**2*llzp)/6d0
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&+ (myi*pi*szp*llzp**2)/2d0 + zeta3
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case(3) !-1-11
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zp = x+1d0
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llzp = log(zp)
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ris = (zp)/2d0 + (zp**2)/32d0 + (zp**3)/216
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&d0 + (zp**4)/1024d0 + (zp**5)/4000d0 + (zp**6)/13824d0
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&+ (zp**7)/43904d0 + (zp**8)/131072d0 + (zp**9)/373248d0
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& + (pi**2*ll2)/12d0 - (ll2**3)/6d0 - (pi**2*llzp)/12d0
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&+ (ll2**2*llzp)/2d0 - (ll2*llzp**2)/2d0 - (7d0*zeta3)/8
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&d0
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case(4) !-10-1
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zp = x+1d0
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llzp = log(zp)
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ris = zp*(2 - llzp) - (pi**2*llzp)/6d0 + zp
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&**4*(1d0/32d0 - (llzp)/16d0) + zp**5*(2d0/125d0 - (llzp
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&)/25d0) + zp**6*(1d0/108d0 - (llzp)/36d0) + zp**7*(2d0/
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&343d0 - (llzp)/49d0) + zp**2*(1d0/4d0 - (llzp)/4d0) + z
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&p**8*(1d0/256d0 - (llzp)/64d0) + zp**9*(2d0/729d0 - (ll
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&zp)/81d0) + zp**3*(2d0/27d0 - (llzp)/9d0) - 2*zeta3
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case(5) !-100
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zp = x+1d0
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llzp = log(zp)
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szp = s(zp)
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ris = (myi*pi**3*szp)/6d0 - myi*pi*szp*zp +
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& (1d0/4d0 - (myi*pi*szp)/4d0)*zp**2 + (1d0/6d0 - (myi*p
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&i*szp)/9d0)*zp**3 + (11d0/96d0 - (myi*pi*szp)/16d0)*zp*
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&*4 + (1d0/12d0 - (myi*pi*szp)/25d0)*zp**5 + (137d0/2160
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&d0 - (myi*pi*szp)/36d0)*zp**6 + (1d0/20d0 - (myi*pi*szp
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&)/49d0)*zp**7 + (363d0/8960d0 - (myi*pi*szp)/64d0)*zp**
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&8 + (761d0/22680d0 - (myi*pi*szp)/81d0)*zp**9 - (pi**2*
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&llzp)/2d0 - zeta3
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case(6) !-101
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zp = x+1d0
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llzp = log(zp)
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ris = zp*ll2 + zp**4*(-(1d0/24d0) + (ll2)/1
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&6d0) + zp**5*(-(131d0/4800d0) + (ll2)/25d0) + zp**6*(-(
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&661d0/34560d0) + (ll2)/36d0) + zp**7*(-(1327d0/94080d0)
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& + (ll2)/49d0) + zp**2*(-(1d0/8d0) + (ll2)/4d0) + zp**8
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&*(-(1163d0/107520d0) + (ll2)/64d0) + zp**9*(-(148969d0/
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&17418240d0) + (ll2)/81d0) + zp**3*(-(5d0/72d0) + (ll2)/
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&9d0) - (pi**2*llzp)/12d0 - (5d0*zeta3)/8d0
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case(7) !-11-1
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zp = x+1d0
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llzp = log(zp)
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ris = -((pi**2*ll2)/6d0) + (ll2**3)/3d0 + (
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&pi**2*llzp)/12d0 - (ll2**2*llzp)/2d0 + zp**8*(-(1d0/655
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&36d0) + (llzp)/16384d0) + zp**2*(-(1d0/16d0) + (llzp)/1
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&6d0) + zp**6*(-(1d0/6912d0) + (llzp)/2304d0) + zp**4*(-
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&(1d0/512d0) + (llzp)/256d0) + zp*(-1 + (llzp)/2d0) + zp
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&**9*(-(1d0/186624d0) + (llzp)/41472d0) + zp**7*(-(1d0/2
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&1952d0) + (llzp)/6272d0) + zp**3*(-(1d0/108d0) + (llzp)
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&/72d0) + zp**5*(-(1d0/2000d0) + (llzp)/800d0) + (7d0*ze
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&ta3)/4d0
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case(8) !-110
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zp = x+1d0
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llzp = log(zp)
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szp = s(zp)
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ris = -((myi*pi**3*szp)/12d0) + (myi*pi*szp
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&*zp)/2d0 + (-(1d0/8d0) + (myi*pi*szp)/16d0)*zp**2 + (-(
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&1d0/18d0) + (myi*pi*szp)/72d0)*zp**3 + (-(5d0/192d0) +
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&(myi*pi*szp)/256d0)*zp**4 + (-(1d0/75d0) + (myi*pi*szp)
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&/800d0)*zp**5 + (-(1d0/135d0) + (myi*pi*szp)/2304d0)*zp
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&**6 + (-(13d0/2940d0) + (myi*pi*szp)/6272d0)*zp**7 + (-
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&(151d0/53760d0) + (myi*pi*szp)/16384d0)*zp**8 + (-(16d0
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&/8505d0) + (myi*pi*szp)/41472d0)*zp**9 - (pi**2*ll2)/4d
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&0 + (myi*pi*szp*ll2**2)/2d0 + (pi**2*llzp)/12d0 - myi*p
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&i*szp*ll2*llzp + (13d0*zeta3)/8d0
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case(9) !-111
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zp = x+1d0
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llzp = log(zp)
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ris = (pi**2*ll2)/12d0 - (zp*ll2)/2d0 - (ll
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&2**3)/3d0 + zp**8*(363d0/2293760d0 - (ll2)/16384d0) + z
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&p**2*(1d0/16d0 - (ll2)/16d0) + zp**6*(137d0/138240d0 -
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&(ll2)/2304d0) + zp**4*(11d0/1536d0 - (ll2)/256d0) + zp*
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&*9*(761d0/11612160d0 - (ll2)/41472d0) + zp**7*(1d0/2560
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&d0 - (ll2)/6272d0) + zp**3*(1d0/48d0 - (ll2)/72d0) + zp
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&**5*(1d0/384d0 - (ll2)/800d0) + (ll2**2*llzp)/2d0 - (ze
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&ta3)/8d0
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case(10) !0-1-1
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zp = x+1d0
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llzp = log(zp)
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ris = zp**5*(-(1d0/125d0) + (llzp)/25d0 - (
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&llzp**2)/10d0) + zp**6*(-(1d0/216d0) + (llzp)/36d0 - (l
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&lzp**2)/12d0) + zp**7*(-(1d0/343d0) + (llzp)/49d0 - (ll
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&zp**2)/14d0) + zp**8*(-(1d0/512d0) + (llzp)/64d0 - (llz
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&p**2)/16d0) + zp**9*(-(1d0/729d0) + (llzp)/81d0 - (llzp
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&**2)/18d0) + zp*(-1 + llzp - (llzp**2)/2d0) + zp**2*(-(
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&1d0/8d0) + (llzp)/4d0 - (llzp**2)/4d0) + zp**3*(-(1d0/2
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&7d0) + (llzp)/9d0 - (llzp**2)/6d0) + zp**4*(-(1d0/64d0)
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& + (llzp)/16d0 - (llzp**2)/8d0) + zeta3
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case(11) !0-10
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zp = x+1d0
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llzp = log(zp)
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szp = s(zp)
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ris = -((myi*pi**3*szp)/6d0) + zp*(-((pi**2
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&)/6d0) + myi*pi*szp - myi*pi*szp*llzp) + zp**2*(-((pi**
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&2)/12d0) + 1d0/2d0 + (myi*pi*szp)/4d0 - (myi*pi*szp*llz
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&p)/2d0) + zp**3*(-((pi**2)/18d0) + 5d0/12d0 + (myi*pi*s
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&zp)/9d0 - (myi*pi*szp*llzp)/3d0) + zp**4*(-((pi**2)/24d
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&0) + 49d0/144d0 + (myi*pi*szp)/16d0 - (myi*pi*szp*llzp)
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&/4d0) + zp**5*(-((pi**2)/30d0) + 41d0/144d0 + (myi*pi*s
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&zp)/25d0 - (myi*pi*szp*llzp)/5d0) + zp**6*(-((pi**2)/36
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&d0) + 5269d0/21600d0 + (myi*pi*szp)/36d0 - (myi*pi*szp*
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&llzp)/6d0) + zp**7*(-((pi**2)/42d0) + 767d0/3600d0 + (m
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&yi*pi*szp)/49d0 - (myi*pi*szp*llzp)/7d0) + zp**8*(26668
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&1d0/1411200d0 - (pi**2)/48d0 + (myi*pi*szp)/64d0 - (myi
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&*pi*szp*llzp)/8d0) + zp**9*(-((pi**2)/54d0) + 1077749d0
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&/6350400d0 + (myi*pi*szp)/81d0 - (myi*pi*szp*llzp)/9d0)
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& + 2*zeta3
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case(12) !0-11
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zp = x+1d0
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llzp = log(zp)
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ris = (pi**2*ll2)/4d0 + zp*((pi**2)/12d0 -
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&ll2 - (ll2**2)/2d0 + ll2*llzp) + zp**2*((pi**2)/24d0 -
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&1d0/4d0 - (ll2)/4d0 - (ll2**2)/4d0 + (ll2*llzp)/2d0) +
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&zp**3*((pi**2)/36d0 - 3d0/16d0 - (ll2)/9d0 - (ll2**2)/6
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&d0 + (ll2*llzp)/3d0) + zp**4*((pi**2)/48d0 - 83d0/576d0
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& - (ll2)/16d0 - (ll2**2)/8d0 + (ll2*llzp)/4d0) + zp**5*
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&(-(1337d0/11520d0) + (pi**2)/60d0 - (ll2)/25d0 - (ll2**
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&2)/10d0 + (ll2*llzp)/5d0) + zp**6*(-(33497d0/345600d0)
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&+ (pi**2)/72d0 - (ll2)/36d0 - (ll2**2)/12d0 + (ll2*llzp
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&)/6d0) + zp**7*(-(5587d0/67200d0) + (pi**2)/84d0 - (ll2
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&)/49d0 - (ll2**2)/14d0 + (ll2*llzp)/7d0) + zp**8*(-(136
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&919d0/1881600d0) + (pi**2)/96d0 - (ll2)/64d0 - (ll2**2)
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&/16d0 + (ll2*llzp)/8d0) + zp**9*((pi**2)/108d0 - 350549
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&39d0/541900800d0 - (ll2)/81d0 - (ll2**2)/18d0 + (ll2*ll
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&zp)/9d0) - zeta3
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case(13) !00-1
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zp = x+1d0
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llzp = log(zp)
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ris = (pi**2*zp)/6d0 + zp**4*((pi**2)/24d0
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&- 131d0/288d0 + (11d0*llzp)/24d0) + zp**2*((pi**2)/12d0
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& - 3d0/4d0 + (llzp)/2d0) + zp**3*((pi**2)/18d0 - 7d0/12
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&d0 + (llzp)/2d0) + zp**6*((pi**2)/36d0 - 2213d0/7200d0
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&+ (137d0*llzp)/360d0) + zp**8*((pi**2)/48d0 - 647707d0/
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&2822400d0 + (363d0*llzp)/1120d0) + zp**5*((pi**2)/30d0
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&- 53d0/144d0 + (5d0*llzp)/12d0) + zp**9*((pi**2)/54d0 -
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& 1290829d0/6350400d0 + (761d0*llzp)/2520d0) + zp**7*((p
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&i**2)/42d0 - 947d0/3600d0 + (7d0*llzp)/20d0) - zeta3
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case(14) !000
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zp = x+1d0
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szp = s(zp)
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ris = -((myi*pi**3*szp)/6d0) + (pi**2*zp)/2
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&d0 + ((pi**2)/4d0 + (myi*pi*szp)/2d0)*zp**2 + (-(1d0/6d
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&0) + (pi**2)/6d0 + (myi*pi*szp)/2d0)*zp**3 + (-(1d0/4d0
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&) + (pi**2)/8d0 + (myi*pi*11d0*szp)/24d0)*zp**4 + ((pi*
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&*2)/10d0 - 7d0/24d0 + (myi*pi*5d0*szp)/12d0)*zp**5 + ((
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&pi**2)/12d0 - 5d0/16d0 + (myi*pi*137d0*szp)/360d0)*zp**
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&6 + ((pi**2)/14d0 - 29d0/90d0 + (myi*pi*7d0*szp)/20d0)*
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&zp**7 + ((pi**2)/16d0 - 469d0/1440d0 + (myi*pi*363d0*sz
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&p)/1120d0)*zp**8 + ((pi**2)/18d0 - 29531d0/90720d0 + (m
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&yi*pi*761d0*szp)/2520d0)*zp**9
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case(15) !001
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zp = x+1d0
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ris = (pi**2*zp)/12d0 + zp**4*((pi**2)/48d0
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& + 11d0/96d0 - (11d0*ll2)/24d0) + zp**2*((pi**2)/24d0 -
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& (ll2)/2d0) + zp**3*(1d0/12d0 + (pi**2)/36d0 - (ll2)/2d
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&0) + zp**6*((pi**2)/72d0 + 731d0/5760d0 - (137d0*ll2)/3
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&60d0) + zp**8*(3931d0/32256d0 + (pi**2)/96d0 - (363d0*l
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&l2)/1120d0) + zp**5*((pi**2)/60d0 + 1d0/8d0 - (5d0*ll2)
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&/12d0) + zp**9*((pi**2)/108d0 + 42799d0/362880d0 - (761
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&d0*ll2)/2520d0) + zp**7*(721d0/5760d0 + (pi**2)/84d0 -
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&(7d0*ll2)/20d0) - (3d0*zeta3)/4d0
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case(16) !01-1
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zp = x+1d0
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llzp = log(zp)
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ris = -((pi**2*ll2)/4d0) + zp*(-((pi**2)/12
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&d0) + (ll2**2)/2d0) + zp**8*(314543d0/3763200d0 - (pi**
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&2)/96d0 + (ll2**2)/16d0 - (1163d0*llzp)/13440d0) + zp**
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&7*(-((pi**2)/84d0) + 953d0/9800d0 + (ll2**2)/14d0 - (13
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&27d0*llzp)/13440d0) + zp**9*(-((pi**2)/108d0) + 3572057
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&71d0/4877107200d0 + (ll2**2)/18d0 - (148969d0*llzp)/193
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&5360d0) + zp**2*(-((pi**2)/24d0) + 3d0/8d0 + (ll2**2)/4
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&d0 - (llzp)/4d0) + zp**3*(-((pi**2)/36d0) + 37d0/144d0
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&+ (ll2**2)/6d0 - (5d0*llzp)/24d0) + zp**6*(13369d0/1152
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&00d0 - (pi**2)/72d0 + (ll2**2)/12d0 - (661d0*llzp)/5760
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&d0) + zp**4*(-((pi**2)/48d0) + 107d0/576d0 + (ll2**2)/8
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&d0 - (llzp)/6d0) + zp**5*(-((pi**2)/60d0) + 8257d0/5760
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&0d0 + (ll2**2)/10d0 - (131d0*llzp)/960d0) + (13d0*zeta3
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&)/8d0
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case(17) !010
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zp = x+1d0
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szp = s(zp)
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ris = -((myi*pi**3*szp)/12d0) + zp*(-((pi**
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&2)/12d0) + myi*pi*szp*ll2) + zp**2*(-((pi**2)/24d0) - (
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&myi*pi*szp)/4d0 + (myi*pi*szp*ll2)/2d0) + zp**3*(1d0/12
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&d0 - (pi**2)/36d0 - (myi*pi*5d0*szp)/24d0 + (myi*pi*szp
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&*ll2)/3d0) + zp**4*(-((pi**2)/48d0) + 5d0/48d0 - (myi*p
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&i*szp)/6d0 + (myi*pi*szp*ll2)/4d0) + zp**5*(5d0/48d0 -
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&(pi**2)/60d0 - (myi*pi*131d0*szp)/960d0 + (myi*pi*szp*l
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&l2)/5d0) + zp**6*(47d0/480d0 - (pi**2)/72d0 - (myi*pi*6
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&61d0*szp)/5760d0 + (myi*pi*szp*ll2)/6d0) + zp**7*(13d0/
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&144d0 - (pi**2)/84d0 - (myi*pi*1327d0*szp)/13440d0 + (m
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&yi*pi*szp*ll2)/7d0) + zp**8*(3341d0/40320d0 - (pi**2)/9
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&6d0 - (myi*pi*1163d0*szp)/13440d0 + (myi*pi*szp*ll2)/8d
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&0) + zp**9*(13817d0/181440d0 - (pi**2)/108d0 - (myi*pi*
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&148969d0*szp)/1935360d0 + (myi*pi*szp*ll2)/9d0) + (3d0*
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&zeta3)/2d0
|
|
|
|
case(18) !011
|
|
|
|
zp = x+1d0
|
|
|
|
ris = -((zp*ll2**2)/2d0) + zp**5*(-(83d0/19
|
|
&20d0) + (131d0*ll2)/960d0 - (ll2**2)/10d0) + zp**6*(-(1
|
|
&1d0/288d0) + (661d0*ll2)/5760d0 - (ll2**2)/12d0) + zp**
|
|
&7*(-(5417d0/161280d0) + (1327d0*ll2)/13440d0 - (ll2**2)
|
|
&/14d0) + zp**8*(-(137d0/4608d0) + (1163d0*ll2)/13440d0
|
|
&- (ll2**2)/16d0) + zp**9*(-(617027d0/23224320d0) + (148
|
|
&969d0*ll2)/1935360d0 - (ll2**2)/18d0) + zp**2*((ll2)/4d
|
|
&0 - (ll2**2)/4d0) + zp**3*(-(1d0/24d0) + (5d0*ll2)/24d0
|
|
& - (ll2**2)/6d0) + zp**4*(-(3d0/64d0) + (ll2)/6d0 - (ll
|
|
&2**2)/8d0) + (zeta3)/8d0
|
|
|
|
case(19) !1-1-1
|
|
|
|
zp = x+1d0
|
|
llzp = log(zp)
|
|
|
|
ris = (pi**2*ll2)/12d0 - (ll2**3)/6d0 + zp*
|
|
&*4*(1d0/1024d0 - (llzp)/256d0 + (llzp**2)/128d0) + zp**
|
|
&2*(1d0/32d0 - (llzp)/16d0 + (llzp**2)/16d0) + zp**7*(1d
|
|
&0/43904d0 - (llzp)/6272d0 + (llzp**2)/1792d0) + zp**5*(
|
|
&1d0/4000d0 - (llzp)/800d0 + (llzp**2)/320d0) + zp**8*(1
|
|
&d0/131072d0 - (llzp)/16384d0 + (llzp**2)/4096d0) + zp**
|
|
&3*(1d0/216d0 - (llzp)/72d0 + (llzp**2)/48d0) + zp*(1d0/
|
|
&2d0 - (llzp)/2d0 + (llzp**2)/4d0) + zp**6*(1d0/13824d0
|
|
&- (llzp)/2304d0 + (llzp**2)/768d0) + zp**9*(1d0/373248d
|
|
&0 - (llzp)/41472d0 + (llzp**2)/9216d0) - (7d0*zeta3)/8d
|
|
&0
|
|
|
|
case(20) !1-10
|
|
|
|
zp = x+1d0
|
|
llzp = log(zp)
|
|
szp = s(zp)
|
|
|
|
ris = (myi*pi**3*szp)/12d0 + (pi**2*ll2)/12
|
|
&d0 - (myi*pi*szp*ll2**2)/2d0 + zp**5*(-(11d0/360d0) + (
|
|
&pi**2)/960d0 - (myi*pi*szp)/800d0 + (myi*pi*szp*llzp)/1
|
|
&60d0) + zp**8*((pi**2)/12288d0 - 9701d0/1881600d0 - (my
|
|
&i*pi*szp)/16384d0 + (myi*pi*szp*llzp)/2048d0) + zp**3*(
|
|
&(pi**2)/144d0 - 1d0/8d0 - (myi*pi*szp)/72d0 + (myi*pi*s
|
|
&zp*llzp)/24d0) + zp*((pi**2)/12d0 - (myi*pi*szp)/2d0 +
|
|
&(myi*pi*szp*llzp)/2d0) + zp**6*((pi**2)/2304d0 - 347d0/
|
|
&21600d0 - (myi*pi*szp)/2304d0 + (myi*pi*szp*llzp)/384d0
|
|
&) + zp**9*((pi**2)/27648d0 - 209d0/66150d0 - (myi*pi*sz
|
|
&p)/41472d0 + (myi*pi*szp*llzp)/4608d0) + zp**4*((pi**2)
|
|
&/384d0 - 35d0/576d0 - (myi*pi*szp)/256d0 + (myi*pi*szp*
|
|
&llzp)/64d0) + zp**7*(-(149d0/16800d0) + (pi**2)/5376d0
|
|
&- (myi*pi*szp)/6272d0 + (myi*pi*szp*llzp)/896d0) + zp**
|
|
&2*((pi**2)/48d0 - 1d0/4d0 - (myi*pi*szp)/16d0 + (myi*pi
|
|
&*szp*llzp)/8d0) - zeta3
|
|
|
|
case(21) !1-11
|
|
|
|
zp = x+1d0
|
|
llzp = log(zp)
|
|
|
|
ris = -((pi**2*ll2)/12d0) + (ll2**3)/6d0 +
|
|
&zp**5*(-((pi**2)/1920d0) + 41d0/4608d0 + (ll2)/800d0 +
|
|
&(ll2**2)/320d0 - (ll2*llzp)/160d0) + zp**8*(-((pi**2)/2
|
|
&4576d0) + 266681d0/361267200d0 + (ll2)/16384d0 + (ll2**
|
|
&2)/4096d0 - (ll2*llzp)/2048d0) + zp**3*(-((pi**2)/288d0
|
|
&) + 5d0/96d0 + (ll2)/72d0 + (ll2**2)/48d0 - (ll2*llzp)/
|
|
&24d0) + zp*(-((pi**2)/24d0) + (ll2)/2d0 + (ll2**2)/4d0
|
|
&- (ll2*llzp)/2d0) + zp**6*(-((pi**2)/4608d0) + 5269d0/1
|
|
&382400d0 + (ll2)/2304d0 + (ll2**2)/768d0 - (ll2*llzp)/3
|
|
&84d0) + zp**9*(1077749d0/3251404800d0 - (pi**2)/55296d0
|
|
& + (ll2)/41472d0 + (ll2**2)/9216d0 - (ll2*llzp)/4608d0)
|
|
& + zp**4*(49d0/2304d0 - (pi**2)/768d0 + (ll2)/256d0 + (
|
|
&ll2**2)/128d0 - (ll2*llzp)/64d0) + zp**7*(-((pi**2)/107
|
|
&52d0) + 767d0/460800d0 + (ll2)/6272d0 + (ll2**2)/1792d0
|
|
& - (ll2*llzp)/896d0) + zp**2*(1d0/8d0 - (pi**2)/96d0 +
|
|
&(ll2)/16d0 + (ll2**2)/16d0 - (ll2*llzp)/8d0) + (zeta3)/
|
|
&4d0
|
|
|
|
case(22) !10-1
|
|
|
|
zp = x+1d0
|
|
llzp = log(zp)
|
|
|
|
ris = -((pi**2*zp)/12d0) + (pi**2*ll2)/6d0
|
|
&+ zp**5*(79d0/1800d0 - (pi**2)/960d0 - (llzp)/15d0) + z
|
|
&p**7*(521d0/39200d0 - (pi**2)/5376d0 - (13d0*llzp)/420d
|
|
&0) + zp**6*(-((pi**2)/2304d0) + 169d0/7200d0 - (2d0*llz
|
|
&p)/45d0) + zp**2*(-((pi**2)/48d0) + 3d0/8d0 - (llzp)/4d
|
|
&0) + zp**4*(25d0/288d0 - (pi**2)/384d0 - (5d0*llzp)/48d
|
|
&0) + zp**8*(-((pi**2)/12288d0) + 7493d0/940800d0 - (151
|
|
&d0*llzp)/6720d0) + zp**3*(-((pi**2)/144d0) + 13d0/72d0
|
|
&- (llzp)/6d0) + zp**9*(-((pi**2)/27648d0) + 3001d0/5953
|
|
&50d0 - (16d0*llzp)/945d0) - (5d0*zeta3)/8d0
|
|
|
|
case(23) !100
|
|
|
|
zp = x+1d0
|
|
szp = s(zp)
|
|
|
|
ris = (myi*pi**3*szp)/12d0 - (pi**2*zp)/4d0
|
|
& + (-((pi**2)/16d0) - (myi*pi*szp)/4d0)*zp**2 + (1d0/12
|
|
&d0 - (pi**2)/48d0 - (myi*pi*szp)/6d0)*zp**3 + (-((pi**2
|
|
&)/128d0) + 3d0/32d0 - (myi*pi*5d0*szp)/48d0)*zp**4 + (1
|
|
&d0/12d0 - (pi**2)/320d0 - (myi*pi*szp)/15d0)*zp**5 + (5
|
|
&d0/72d0 - (pi**2)/768d0 - (myi*pi*2d0*szp)/45d0)*zp**6
|
|
&+ (-((pi**2)/1792d0) + 41d0/720d0 - (myi*pi*13d0*szp)/4
|
|
&20d0)*zp**7 + (-((pi**2)/4096d0) + 539d0/11520d0 - (myi
|
|
&*pi*151d0*szp)/6720d0)*zp**8 + (22d0/567d0 - (pi**2)/92
|
|
&16d0 - (myi*pi*16d0*szp)/945d0)*zp**9 + (pi**2*ll2)/2d0
|
|
& - (3d0*zeta3)/4d0
|
|
|
|
case(24) !101
|
|
|
|
zp = x+1d0
|
|
|
|
ris = -((pi**2*zp)/24d0) + (pi**2*ll2)/12d0
|
|
& + zp**5*(-((pi**2)/1920d0) - 1d0/30d0 + (ll2)/15d0) +
|
|
&zp**7*(-((pi**2)/10752d0) - 767d0/40320d0 + (13d0*ll2)/
|
|
&420d0) + zp**6*(-((pi**2)/4608d0) - 97d0/3840d0 + (2d0*
|
|
&ll2)/45d0) + zp**2*(-((pi**2)/96d0) + (ll2)/4d0) + zp**
|
|
&4*(-(1d0/24d0) - (pi**2)/768d0 + (5d0*ll2)/48d0) + zp**
|
|
&8*(-((pi**2)/24576d0) - 935d0/64512d0 + (151d0*ll2)/672
|
|
&0d0) + zp**3*(-(1d0/24d0) - (pi**2)/288d0 + (ll2)/6d0)
|
|
&+ zp**9*(-(2041d0/181440d0) - (pi**2)/55296d0 + (16d0*l
|
|
&l2)/945d0) - (zeta3)/4d0
|
|
|
|
case(25) !11-1
|
|
|
|
zp = x+1d0
|
|
llzp = log(zp)
|
|
|
|
ris = (ll2**3)/6d0 + zp*((pi**2)/24d0 - (ll
|
|
&2**2)/4d0) + zp**3*((pi**2)/288d0 - 7d0/96d0 - (ll2**2)
|
|
&/48d0 + (llzp)/16d0) + zp**6*(-(2213d0/460800d0) + (pi*
|
|
&*2)/4608d0 - (ll2**2)/768d0 + (137d0*llzp)/23040d0) + z
|
|
&p**8*((pi**2)/24576d0 - 647707d0/722534400d0 - (ll2**2)
|
|
&/4096d0 + (363d0*llzp)/286720d0) + zp**4*(-(131d0/4608d
|
|
&0) + (pi**2)/768d0 - (ll2**2)/128d0 + (11d0*llzp)/384d0
|
|
&) + zp**5*((pi**2)/1920d0 - 53d0/4608d0 - (ll2**2)/320d
|
|
&0 + (5d0*llzp)/384d0) + zp**9*(-(1290829d0/3251404800d0
|
|
&) + (pi**2)/55296d0 - (ll2**2)/9216d0 + (761d0*llzp)/12
|
|
&90240d0) + zp**7*((pi**2)/10752d0 - 947d0/460800d0 - (l
|
|
&l2**2)/1792d0 + (7d0*llzp)/2560d0) + zp**2*(-(3d0/16d0)
|
|
& + (pi**2)/96d0 - (ll2**2)/16d0 + (llzp)/8d0) - (zeta3)
|
|
&/8d0
|
|
|
|
case(26) !110
|
|
|
|
zp = x+1d0
|
|
szp = s(zp)
|
|
|
|
ris = -((pi**2*ll2)/12d0) + (myi*pi*szp*ll2
|
|
&**2)/2d0 + zp**5*((pi**2)/1920d0 - 1d0/40d0 + (myi*pi*5
|
|
&d0*szp)/384d0 - (myi*pi*szp*ll2)/160d0) + zp**8*(-(1019
|
|
&d0/161280d0) + (pi**2)/24576d0 + (myi*pi*363d0*szp)/286
|
|
&720d0 - (myi*pi*szp*ll2)/2048d0) + zp**3*(-(1d0/24d0) +
|
|
& (pi**2)/288d0 + (myi*pi*szp)/16d0 - (myi*pi*szp*ll2)/2
|
|
&4d0) + zp*((pi**2)/24d0 - (myi*pi*szp*ll2)/2d0) + zp**6
|
|
&*(-(23d0/1440d0) + (pi**2)/4608d0 + (myi*pi*137d0*szp)/
|
|
&23040d0 - (myi*pi*szp*ll2)/384d0) + zp**9*((pi**2)/5529
|
|
&6d0 - 23d0/5670d0 + (myi*pi*761d0*szp)/1290240d0 - (myi
|
|
&*pi*szp*ll2)/4608d0) + zp**4*((pi**2)/768d0 - 7d0/192d0
|
|
& + (myi*pi*11d0*szp)/384d0 - (myi*pi*szp*ll2)/64d0) + z
|
|
&p**7*(-(101d0/10080d0) + (pi**2)/10752d0 + (myi*pi*7d0*
|
|
&szp)/2560d0 - (myi*pi*szp*ll2)/896d0) + zp**2*((pi**2)/
|
|
&96d0 + (myi*pi*szp)/8d0 - (myi*pi*szp*ll2)/8d0) + (zeta
|
|
&3)/8d0
|
|
|
|
case(27) !111
|
|
|
|
zp = x+1d0
|
|
|
|
ris = (zp*ll2**2)/4d0 - (ll2**3)/6d0 + zp**
|
|
&4*(1d0/64d0 - (11d0*ll2)/384d0 + (ll2**2)/128d0) + zp**
|
|
&2*(-((ll2)/8d0) + (ll2**2)/16d0) + zp**7*(29d0/11520d0
|
|
&- (7d0*ll2)/2560d0 + (ll2**2)/1792d0) + zp**5*(7d0/768d
|
|
&0 - (5d0*ll2)/384d0 + (ll2**2)/320d0) + zp**8*(469d0/36
|
|
&8640d0 - (363d0*ll2)/286720d0 + (ll2**2)/4096d0) + zp**
|
|
&3*(1d0/48d0 - (ll2)/16d0 + (ll2**2)/48d0) + zp**6*(5d0/
|
|
&1024d0 - (137d0*ll2)/23040d0 + (ll2**2)/768d0) + zp**9*
|
|
&(29531d0/46448640d0 - (761d0*ll2)/1290240d0 + (ll2**2)/
|
|
&9216d0)
|
|
c End of expansions around x = -1
|
|
|
|
end select
|
|
c --- set the imaginary part back to zero if it has been modified to
|
|
c --- get the branch cuts right (and should be zero).
|
|
if (bcflag.eq.1) then
|
|
xre = dreal(x)
|
|
if (n3.eq.0.and.xre.gt.0d0) then
|
|
if (xre.lt.1d0) then
|
|
ris = dcmplx(dreal(ris),0d0)
|
|
endif
|
|
c
|
|
else if (n3.eq.1.and.xre.lt.1d0) then
|
|
if (n1.ne.-1.and.n2.ne.-1) then
|
|
ris = dcmplx(dreal(ris),0d0)
|
|
else if (xre.gt.-1d0) then
|
|
ris = dcmplx(dreal(ris),0d0)
|
|
endif
|
|
c
|
|
else if (n3.eq.-1.and.xre.gt.-1d0) then
|
|
if (n1.ne.1.and.n2.ne.1) then
|
|
ris = dcmplx(dreal(ris),0d0)
|
|
else if (xre.lt.1d0) then
|
|
ris = dcmplx(dreal(ris),0d0)
|
|
endif
|
|
endif
|
|
endif
|
|
|
|
HPL3arm1=ris
|
|
return
|
|
end function
|