The extended Zeilberger algorithm with parameters

DOI10.1016/j.jsc.2011.12.024zbMath1305.33035arXiv0908.1328OpenAlexW1986292888MaRDI QIDQ413409

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

Publication date: 7 May 2012

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

Full work available at URL: https://arxiv.org/abs/0908.1328

zbMATH Keywords

orthogonal polynomialshypergeometric seriesZeilberger's algorithmGosper's algorithmsymbolic summation

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) 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) Hypergeometric functions (33C99)

Related Items (9)

Numerical computations of separability probabilities ⋮ Quasi-orthogonality of some hypergeometric and \(q\)-hypergeometric polynomials ⋮ Recurrence relations for the connection coefficients of classical orthogonal polynomials ⋮ Recurrences for Callan's generalization of Narayana polynomials ⋮ Polynomial reduction and supercongruences ⋮ Formal residue and computer-assisted proofs of combinatorial identities ⋮ Contiguous Relations and Creative Telescoping ⋮ Gosper summability of rational multiples of hypergeometric terms ⋮ Inner bounds for the extreme zeros of ₃F₂ hypergeometric polynomials

Uses Software

• qZeil

Cites Work

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• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• Extended Zeilberger's algorithm for identities on Bernoulli and Euler polynomials
• The method of creative telescoping
• Representations of orthogonal polynomials
• Pfaff's method. I: The Mills-Robbins-Rumsey determinant.
• Pfaff's method. III: Comparison with the WZ method
• Algorithms for \(q\)-hypergeometric summation in computer algebra
• An extension of Zeilberger's fast algorithm to general holonomic functions
• Summation in Finite Terms
• Decision procedure for indefinite hypergeometric summation
• Solving parameterized linear difference equations in terms of indefinite nested sums and products

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