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arXiv · 2005.05612

A Novel Algorithm for Nested Summation and Hypergeometric Expansions

Andrew J. McLeod·Henrik Munch·Georgios Papathanasiou·Matt von Hippel
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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 $O(\epsilon^6)$ in dimensional regularization. We also outline the general telescopic strategy of this algorithm, which we anticipate can be applied to other classes of sums.

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Andrew J. McLeod, Henrik Munch, Georgios Papathanasiou, Matt von Hippel. 2020-05-12. A Novel Algorithm for Nested Summation and Hypergeometric Expansions. https://doi.org/10.1007/jhep11(2020)122

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