A novel algorithm for nested summation and hypergeometric expansions
Research output: Contribution to journal › Journal article › Research › peer-review
Documents
- McLeod2020_Article_ANovelAlgorithmForNestedSummat
Final published version, 608 KB, PDF document
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.
Original language | English |
---|---|
Article number | 122 |
Journal | Journal of High Energy Physics |
Volume | 2020 |
Issue number | 11 |
Number of pages | 35 |
ISSN | 1029-8479 |
DOIs | |
Publication status | Published - 23 Nov 2020 |
- NLO Computations, TRANSCENDENTAL FUNCTIONS, NUMERICAL EVALUATION, SYMBOLIC SUMMATION, MELLIN TRANSFORMS, HARMONIC SUMS, POLYLOGARITHMS, VALUES
Research areas
Number of downloads are based on statistics from Google Scholar and www.ku.dk
ID: 253689077