Simplifying Multiple Sums in Difference Fields
Abstract
In this survey article we present difference field algorithms for symbolic summation. Special emphasize is put on new aspects in how the summation problems are rephrased in terms of difference fields, how the problems are solved there, and how the derived results in the given difference field can be reinterpreted as solutions of the input problem. The algorithms are illustrated with the Mathematica package \SigmaP\ by discovering and proving new harmonic number identities extending those from (Paule and Schneider, 2003). In addition, the newly developed package \texttt{EvaluateMultiSums} is introduced that combines the presented tools. In this way, large scale summation problems for the evaluation of Feynman diagrams in QCD (Quantum ChromoDynamics) can be solved completely automatically.
Keywords
Cite
@article{arxiv.1304.4134,
title = {Simplifying Multiple Sums in Difference Fields},
author = {Carsten Schneider},
journal= {arXiv preprint arXiv:1304.4134},
year = {2013}
}
Comments
Uses svmult.cls, to appear as contribution in the book "Computer Algebra in Quantum Field Theory: Integration, Summation and Special Functions" (www.Springer.com)