Telescoping method, summation formulas, and inversion pairs

DOI10.3934/ERA.2021007zbMath1480.33011OpenAlexW3119623874MaRDI QIDQ2046918

Yarong Wei, Qing-Hu Hou

Publication date: 19 August 2021

Published in: Electronic Research Archive (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/era.2021007

zbMATH Keywords

basic hypergeometric seriestelescoping methodelliptic hypergeometric seriesGosper's algorithminversion pair

Mathematics Subject Classification ID

Combinatorial identities, bijective combinatorics (05A19) (q)-gamma functions, (q)-beta functions and integrals (33D05) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Cites Work

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• The method of creative telescoping
• Generalized bibasic hypergeometric series and their \(U(n)\) extensions
• Summation and transformation formulas for elliptic hypergeometric series.
• Multibasic and mixed hypergeometric Gosper-type algorithms
• An extension of Zeilberger's fast algorithm to general holonomic functions
• The \((f,g)\)-inversion formula and its applications: the \((f,g)\)-summation formula
• A Matrix Inverse
• Summation, Transformation, and Expansion Formulas for Bibasic Series
• Summation in Finite Terms
• Decision procedure for indefinite hypergeometric summation
• A new matrix inverse

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