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A novel algorithm for nested summation and hypergeometric expansions
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DOI：10.1007/JHEP11(2020)122.png)
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摘要
En 中文
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.
Keyword:
NLO Computations
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期刊
IF:
5.5
论文数:
4.0W
被引数:
13.7W
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