Algorithms for \(q\)-hypergeometric summation in computer algebra

DOI10.1006/jsco.1998.0339zbMath0946.65008OpenAlexW2119126401MaRDI QIDQ1971738

Wolfram Koepf, Harald Böing

Publication date: 10 October 2000

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jsco.1998.0339

zbMATH Keywords

\(q\)-series\(q\)-hypergeometric seriesMaple\(q\)-Askey-Wilson polynomialsGosper and Zeilberger algorithmshypergeometric solutions of linear recurrence

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Computation of special functions and constants, construction of tables (65D20) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) (33D45) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (21)

Properties ofq-holonomic functions ⋮ Proof of Andrews' conjecture on a₄φ₃summation ⋮ Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications ⋮ On solutions of holonomic divided-difference equations on nonuniform lattices ⋮ Algorithmic determination of \(q\)-power series for \(q\)-holonomic functions ⋮ The extended Zeilberger algorithm with parameters ⋮ \( m\)-fold hypergeometric solutions of linear recurrence equations revisited ⋮ Applicability of the \(q\)-analogue of Zeilberger's algorithm ⋮ On the Gosper-Petkovšek representation of rational functions ⋮ Classical Orthogonal Polynomials of a Discrete and a q-Discrete Variable ⋮ Computer Algebra, Power Series and Summation ⋮ Rational solutions of ordinary difference equations ⋮ The fourth-order difference equation satisfied by the associated orthogonal polynomials of the Dq-Laguerre - Hahn Class ⋮ The Abel lemma and the \(q\)-Gosper algorithm ⋮ The Abel Lemma and the $q$-Gosper Algorithm ⋮ Parameter augmentation and the \(q\)-Gosper algorithm ⋮ Rational solutions of first-order algebraic ordinary difference equations ⋮ A generalization of the concept of \(q\)-fractional integrals ⋮ Creative Telescoping for Holonomic Functions ⋮ Contiguous relations and summation and transformation formulae for basic hypergeometric series ⋮ MultInt, a MAPLE package for multiple integration by the WZ method

Uses Software

• Maple
• qZeil
• pqTelescope
• SumTools

Cites Work

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• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• Rational solutions of linear difference and \(q\)-differential equations with polynomial coefficients
• On Zeilberger's algorithm and its \(q\)-analogue
• Short and easy computer proofs of the Rogers-Ramanujan identities and of identities of similar type
• A generalization of Gosper's algorithm to bibasic hypergeometric summation
• \(q\)-hypergeometric solutions of \(q\)-difference equations
• Multibasic and mixed hypergeometric Gosper-type algorithms
• Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials

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