A novel algorithm for nested summation and hypergeometric expansions

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Standard

A novel algorithm for nested summation and hypergeometric expansions. / McLeod, Andrew J.; Munch, Henrik Jessen; Papathanasiou, Georgios; von Hippel, Matt.

I: Journal of High Energy Physics, Bind 2020, Nr. 11, 122, 23.11.2020.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt

Harvard

McLeod, AJ, Munch, HJ, Papathanasiou, G & von Hippel, M 2020, 'A novel algorithm for nested summation and hypergeometric expansions', Journal of High Energy Physics, bind 2020, nr. 11, 122. https://doi.org/10.1007/JHEP11(2020)122

APA

McLeod, A. J., Munch, H. J., Papathanasiou, G., & von Hippel, M. (2020). A novel algorithm for nested summation and hypergeometric expansions. Journal of High Energy Physics, 2020(11), [122]. https://doi.org/10.1007/JHEP11(2020)122

Vancouver

McLeod AJ, Munch HJ, Papathanasiou G, von Hippel M. A novel algorithm for nested summation and hypergeometric expansions. Journal of High Energy Physics. 2020 nov. 23;2020(11). 122. https://doi.org/10.1007/JHEP11(2020)122

Author

McLeod, Andrew J. ; Munch, Henrik Jessen ; Papathanasiou, Georgios ; von Hippel, Matt. / A novel algorithm for nested summation and hypergeometric expansions. I: Journal of High Energy Physics. 2020 ; Bind 2020, Nr. 11.

Bibtex

@article{b78e348a2e8b475aa177595bc22ecb7e,
title = "A novel algorithm for nested summation and hypergeometric expansions",
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.",
keywords = "NLO Computations, TRANSCENDENTAL FUNCTIONS, NUMERICAL EVALUATION, SYMBOLIC SUMMATION, MELLIN TRANSFORMS, HARMONIC SUMS, POLYLOGARITHMS, VALUES",
author = "McLeod, {Andrew J.} and Munch, {Henrik Jessen} and Georgios Papathanasiou and {von Hippel}, Matt",
year = "2020",
month = nov,
day = "23",
doi = "10.1007/JHEP11(2020)122",
language = "English",
volume = "2020",
journal = "Journal of High Energy Physics (Online)",
issn = "1126-6708",
publisher = "Springer",
number = "11",

}

RIS

TY - JOUR

T1 - A novel algorithm for nested summation and hypergeometric expansions

AU - McLeod, Andrew J.

AU - Munch, Henrik Jessen

AU - Papathanasiou, Georgios

AU - von Hippel, Matt

PY - 2020/11/23

Y1 - 2020/11/23

N2 - 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.

AB - 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.

KW - NLO Computations

KW - TRANSCENDENTAL FUNCTIONS

KW - NUMERICAL EVALUATION

KW - SYMBOLIC SUMMATION

KW - MELLIN TRANSFORMS

KW - HARMONIC SUMS

KW - POLYLOGARITHMS

KW - VALUES

U2 - 10.1007/JHEP11(2020)122

DO - 10.1007/JHEP11(2020)122

M3 - Journal article

VL - 2020

JO - Journal of High Energy Physics (Online)

JF - Journal of High Energy Physics (Online)

SN - 1126-6708

IS - 11

M1 - 122

ER -

ID: 253689077