A telescoping method for double summations

DOI10.1016/j.cam.2005.10.010zbMath1108.33017arXivmath/0504525OpenAlexW2002069351MaRDI QIDQ2503028

Qing-Hu Hou, William Y. C. Chen, Yan-Ping Mu

Publication date: 13 September 2006

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504525

zbMATH Keywords

Zeilberger's algorithmdouble summationhypergeometric term

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computation of special functions and constants, construction of tables (65D20) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (13)

Constructing minimal telescopers for rational functions in three discrete variables ⋮ An algorithmic approach to the \(q\)-summability problem of bivariate rational functions ⋮ On the summability of bivariate rational functions ⋮ Congruences for sums involving Franel numbers ⋮ Telescoping method and congruences for double sums ⋮ New series for powers of \(\pi\) and related congruences ⋮ Identities and congruences for Catalan–Larcombe–French numbers ⋮ Divisibility results on Franel numbers and related polynomials ⋮ An algorithm for deciding the summability of bivariate rational functions ⋮ On the combinatorics of the Pfaff identity ⋮ On Motzkin numbers and central trinomial coefficients ⋮ Creative Telescoping for Holonomic Functions ⋮ Congruences for Domb and Almkvist-Zudilin numbers

Uses Software

• SIGMA
• Telescopers

Cites Work

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• Multi-variable Zeilberger and Almkvist-Zeilberger algorithms and the sharpening of Wilf-Zeilberger theory
• The method of creative telescoping
• Non-commutative elimination in Ore algebras proves multivariate identities
• Some questions concerning computer-generated proofs of a binomial double- sum identity
• Binomial identities -- combinatorial and algorithmic aspects
• On the structure of multivariate hypergeometric terms.
• \(k\)-free recurrences of double hypergeometric terms
• An extension of Zeilberger's fast algorithm to general holonomic functions
• A new Sigma approach to multi-summation
• Telescoping in the context of symbolic summation in Maple
• Decision procedure for indefinite hypergeometric summation
• A Binomial Identity Arising from a Sorting Problem

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