Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers
Mathematical Physics
2015-06-17 v1 High Energy Physics - Phenomenology
High Energy Physics - Theory
math.MP
Abstract
A survey is given on mathematical structures which emerge in multi-loop Feynman diagrams. These are multiply nested sums, and, associated to them by an inverse Mellin transform, specific iterated integrals. Both classes lead to sets of special numbers. Starting with harmonic sums and polylogarithms we discuss recent extensions of these quantities as cyclotomic, generalized (cyclotomic), and binomially weighted sums, associated iterated integrals and special constants and their relations.
Cite
@article{arxiv.1310.5645,
title = {Generalized Harmonic, Cyclotomic, and Binomial Sums, their Polylogarithms and Special Numbers},
author = {J Ablinger and J Blümlein and C Schneider},
journal= {arXiv preprint arXiv:1310.5645},
year = {2015}
}
Comments
10 pages, Proceedings ACAT 2013