Simon Albino
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] .