## HarmonicSums: A Mathematica Package for dealing with Harmonic Sums, Generalized Harmonic Sums and Cyclotomic Sums and their related Integral Representations

Authors: Jakob Ablinger

### Registration and Legal Notices

The source code for this package is password protected. To get the password send an email to Peter Paule. It will be given for free to all researchers and non-commercial users.Copyright © 1999–2012 The RISC Combinatorics Group, Austria — all rights reserved. Commercial use of the software is prohibited without prior written permission.### A Note on Encoded Files

This package contains one or more Mathematica input files which are encoded. Those files cannot be read or modified directly as plain text, but can be loaded into Mathematica just like any normal input file (i.e., with**<<"**or

*file*"**Get["**). There is no need (and also no way) to decode them by using additional software or a special key.If loading an encoded file causes a syntax error, open it with a text editor and remove any blank lines at the beginning (for some reason your Mac could have inserted them silently...).

*file*"]### The Package

The package is contained in the Mathematica input file- HarmonicSums.m (encoded)

- demo.nb (for Mathematica version 8.0 and 9.0)

- RelTabSinfH1.m
- RelTabSinfH1upto8.m
- RelTabCSinf.m
- RelTab.m
- RelTabStat.m
- RelTabDiff.m
- RelTabHalf.m
- RelTabDiffHalf.m

### Literature

The theoretical background of the algorithms implemented in HarmonicSums is described in- Computer Algebra Algorithms for Special Functions in Particle Physics (PhD Thesis). RISC, Johannes Kepler University, April 2012. [pdf]
- A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics (Diploma Thesis). RISC, Johannes Kepler University, February 2009. [pdf]

- J. Ablinger. A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics. Johannes Kepler University. Diploma Thesis. February 2009. arXiv:1011.1176 [math-ph].
- J. Ablinger. Computer Algebra Algorithms for Special Functions in Particle Physics. Johannes Kepler University. PhD Thesis. April 2012.
- J. Ablinger, J. Blümlein and C. Schneider. Analytic and Algorithmic Aspects of Generalized Harmonic Sums and Polylogarithms. arXiv:1212.xxxx [math-ph].
- J. Ablinger, J. Blümlein and C. Schneider. Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials. J. Math. Phys. 52 (2011) 102301. [arXiv:1105.6063 [math-ph]].
- J. Blümlein. Structural Relations of Harmonic Sums and Mellin Transforms up to Weight w = 5. Comput. Phys. Commun. 180 (2009) 2218. [arXiv:0901.3106 [hep-ph]].
- E. Remiddi and J. A. M. Vermaseren. Harmonic polylogarithms. Int. J. Mod. Phys. A 15 (2000) 725. [hep-ph/9905237].
- J. A. M. Vermaseren. Harmonic sums, Mellin transforms and integrals. Int. J. Mod. Phys. A 14 (1999) 2037. [hep-ph/9806280].