Refined Holonomic Summation Algorithms in Particle Physics

06/12/2017

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by Johannes Blümlein, et al.

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Johannes Kepler University Linz

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DESY

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An improved multi-summation approach is introduced and discussed that enables one to simultaneously handle indefinite nested sums and products in the setting of difference rings and holonomic sequences. Relevant mathematics is reviewed and the underlying advanced difference ring machinery is elaborated upon. The flexibility of this new toolbox contributed substantially to evaluating complicated multi-sums coming from particle physics. Illustrative examples of the functionality of the new software package RhoSum are given.

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Refined Holonomic Summation Algorithms in Particle Physics

Representing (q--)hypergeometric products and mixed versions in difference rings

Refined telescoping algorithms in RΠΣ-extensions to reduce the degrees of the denominators

Computing Mellin representations and asymptotics of nested binomial sums in a symbolic way: the RICA package

Provenance tracking in the LHCb software

Minimal representations and algebraic relations for single nested products

Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation

Representation of hypergeometric products of higher nesting depths in difference rings

Refined Holonomic Summation Algorithms in Particle Physics

Related Research

Representing (q--)hypergeometric products and mixed versions in difference rings

Refined telescoping algorithms in RΠΣ-extensions to reduce the degrees of the denominators

Computing Mellin representations and asymptotics of nested binomial sums in a symbolic way: the RICA package

Provenance tracking in the LHCb software

Minimal representations and algebraic relations for single nested products

Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation

Representation of hypergeometric products of higher nesting depths in difference rings