On Zeilberger's algorithm and its \(q\)-analogue

DOI10.1016/0377-0427(93)90317-5zbMath0797.65011OpenAlexW2070989931MaRDI QIDQ1318445

Koornwinder, Tom H.

Publication date: 27 March 1994

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

Full work available at URL: https://doi.org/10.1016/0377-0427(93)90317-5

zbMATH Keywords

hypergeometric seriescomputer algebraZeilberger's algorithm\(q\)-versionGosper's algorithmexplicit summation formulasMaple V procedures

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) Generalized hypergeometric series, ({}_pF_q) (33C20) Numerical summation of series (65B10) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (34)

\(q\)-Gosper algorithm and simple Bailey pairs ⋮ Construction and implementation of asymptotic expansions for Jacobi-type orthogonal polynomials ⋮ Telescoping in the context of symbolic summation in Maple ⋮ A two-line algorithm for proving \(q\)-hypergeometric identities ⋮ \(q\)-hypergeometric solutions of \(q\)-difference equations ⋮ A representation theorem for (\(q\)-)holonomic sequences ⋮ Pfaffian decomposition and a Pfaffian analogue of \(q\)-Catalan Hankel determinants ⋮ Fast computation of the \(N\)-th term of a \(q\)-holonomic sequence and applications ⋮ A family of WZ pairs and \(q\)-identities ⋮ A direct algorithm to construct the minimal \(Z\)-pairs for rational functions. ⋮ Algorithmic determination of \(q\)-power series for \(q\)-holonomic functions ⋮ \texttt{qMultiSum} -- a package for proving \(q\)-hypergeometric multiple summation identities ⋮ Identities for families of orthogonal polynomials and special functions ⋮ Algorithms for \(q\)-hypergeometric summation in computer algebra ⋮ Applicability of the \(q\)-analogue of Zeilberger's algorithm ⋮ Sharp upper bounds for the orders of the recurrences output by the Zeilberger and \(q\)-Zeilberger algorithms ⋮ On the Gosper-Petkovšek representation of rational functions ⋮ Multibasic and mixed hypergeometric Gosper-type algorithms ⋮ The \(C\)-polynomial of a knot ⋮ A simple proof of Bailey’s very-well-poised ₆𝜓₆ summation ⋮ SIMPLIFYING SUMS IN ΠΣ*-EXTENSIONS ⋮ The Abel lemma and the \(q\)-Gosper algorithm ⋮ The Abel Lemma and the $q$-Gosper Algorithm ⋮ Parameter augmentation and the \(q\)-Gosper algorithm ⋮ Proving hypergeometric identities by numerical verifications ⋮ THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS ⋮ NUMERICAL SPECTRAL LEGENDRE APPROACH FOR SOLVING SPACE-TIME FRACTIONAL ADVECTION-DISPERSION PROBLEMS ⋮ The \(q\)-WZ method for infinite series ⋮ Rogers-Ramanujan computer searches ⋮ A Mathematica package for \(q\)-holonomic sequences and power series ⋮ Creative Telescoping for Holonomic Functions ⋮ Simplifying Multiple Sums in Difference Fields ⋮ \(q\)-rational reduction and \(q\)-analogues of series for \(\pi\) ⋮ Gosper summability of rational multiples of hypergeometric terms

Uses Software

• Maple

Cites Work

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• A fast algorithm for proving terminating hypergeometric identities
• A holonomic systems approach to special functions identities
• The method of creative telescoping
• Hypergeometric solutions of linear recurrences with polynomial coefficients
• Decision procedure for indefinite hypergeometric summation
• Generalized Hypergeometric Function of Unit Argument

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