Evaluation of Binomial Double Sums Involving Absolute Values

DOI10.1007/978-3-030-44559-1_14OpenAlexW2482032014MaRDI QIDQ3387114

Carsten Schneider, Christian Krattenthaler

Publication date: 12 January 2021

Published in: Algorithmic Combinatorics: Enumerative Combinatorics, Special Functions and Computer Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.05314

zbMATH Keywords

Gosper algorithmnested sumsChu-Vandermonde summationdifference ringsbinomial double sumsDixon's summationhypergeometric double sums

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30)

Related Items (3)

Hypergeometric structures in Feynman integrals ⋮ Some Double Sums Involving Ratios of Binomial Coefficients Arising From Urn Models ⋮ Term Algebras, Canonical Representations and Difference Ring Theory for Symbolic Summation

Uses Software

• SIGMA
• EvaluateMultiSums

Cites Work

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• Multiple binomial sums
• A difference ring theory for symbolic summation
• Discrete analogues of Macdonald-Mehta integrals
• Summation theory. II: Characterizations of \(R {\Pi}{\Sigma}^{\ast}\)-extensions and algorithmic aspects
• Sone new inverse series relations
• A \textit{Mathematica} version of Zeilberger's algorithm for proving binomial coefficient identities
• Symbolic summation assists combinatorics
• Some binomial sums involving absolute values
• Summation in Finite Terms
• Decision procedure for indefinite hypergeometric summation
• A new matrix inverse
• Simplifying Multiple Sums in Difference Fields

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