Simon Albino




The programs for calculating harmonic sums analytically and numerically according to the method of Phys. Lett. B674 (2009) 41 (arXiv:0902.2148 [hep-ph]) are provided at the links to the right. The calculations are limited to all harmonic sums with weights less than and equal to 5, but can be straightforwardly extended to all higher weights.

If you use these routines, I would be grateful if you could let me know at the email address below, and don't forget to cite arXiv:0902.2148 [hep-ph]. In particular, please let me know if you implement any improvements.

FORTRAN routines

Type "tar zxvf HS.tar.gz" and then "cd HS". In addition to the main routines, which are all in "HS.f", an example program, "HarmonicSums.f", is provided to illustrate how to use them, which compares numerically each continued harmonic sum with the result obtained from its definition for integer argument. Compile everything with "./compile", which uses pgf77 although any fortran compiler should suffice.

The series for the harmonic sums, in the "s*.f" files, were calculated to O(1/N^20), but can be recalculated to higher accuracy if required (you can also do this yourself by rerunning the master mathematica file with the variable "EL" increased). If you just need more accuracy, increase the number "32.d0" (appearing after the line that reads
"c     Increase this number (32.d0) for more accuracy" in "HS.f").

Master Mathematica file

This program, "HarmonicSums.nb" (WHICH WORKS UNDER MATHEMATICA 6 ONLY - Mathematica 7 users should use this version instead), implements the method of Phys. Lett. B674 (2009) 41, and is the program from which all FORTRAN expressions (in the "s*.f" files) for the harmonic sums are obtained. For the FORTRAN code generation, you will need the file "Format.m" (in the same directory as "HarmonicSums.nb"), obtainable here.

The large-n expansions for the harmonic sums are contained in the array "sGen", i.e. and e.g. sGen[1,2,-1,0,0] .


Please send any comments / suggestions / problems etc. to me at simon(a)mail.desy.de