City Research Online

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


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 > Mathematics
SWORD Depositor:
[thumbnail of JHEP11(2020)122.pdf]
Text - Published Version
Available under License Creative Commons: Attribution International Public License 4.0.

Download (622kB) | Preview


Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email


Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login