A novel algorithm for nested summation and hypergeometric expansions
McLeod, A. J., Munch, H. J., Papathanasiou, G. 
ORCID: 0000-0002-2627-9906 & von Hippel, M. (2020).
A novel algorithm for nested summation and hypergeometric expansions.
Journal of High Energy Physics, 2020(11),
article number 122.
doi: 10.1007/jhep11(2020)122
Abstract
We consider a class of sums over products of Z-sums whose arguments differ by a symbolic integer. Such sums appear, for instance, in the expansion of Gauss hypergeometric functions around integer indices that depend on a symbolic parameter. We present a telescopic algorithm for efficiently converting these sums into generalized polylogarithms, Z-sums, and cyclotomic harmonic sums for generic values of this parameter. This algorithm is illustrated by computing the double pentaladder integrals through ten loops, and a family of massive self-energy diagrams through
| Publication Type: | Article |
|---|---|
| Additional Information: | This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. |
| Publisher Keywords: | NLO Computations |
| Subjects: | Q Science > QA Mathematics |
| Departments: | School of Science & Technology School of Science & Technology > Department of Mathematics |
| SWORD Depositor: |
Available under License Creative Commons: Attribution International Public License 4.0.
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