A criterion for the applicability of Zeilberger's algorithm to rational functions

DOI10.1016/S0012-365X(02)00442-9zbMath1023.33017OpenAlexW2034438073MaRDI QIDQ1861199

Yanyan Li

Publication date: 16 March 2003

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0012-365x(02)00442-9

zbMATH Keywords

rational function\(q\)-difference operatorZeilberger's algorithmlinear difference operatorhypergeometric termdecomposition of indefinite sumterminating condition

Mathematics Subject Classification ID

Classical hypergeometric functions, ({}_2F_1) (33C05) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items (15)

Efficient rational creative telescoping ⋮ Telescoping in the context of symbolic summation in Maple ⋮ Deconstructing the Zeilberger algorithm^† ⋮ Constructing minimal telescopers for rational functions in three discrete variables ⋮ Some open problems related to creative telescoping ⋮ A direct algorithm to construct the minimal \(Z\)-pairs for rational functions. ⋮ Telescopers for differential forms with one parameter ⋮ Residues and telescopers for bivariate rational functions ⋮ On the existence of telescopers for mixed hypergeometric terms ⋮ Applicability of the \(q\)-analogue of Zeilberger's algorithm ⋮ On the existence of telescopers for rational functions in three variables ⋮ Efficient \(q\)-integer linear decomposition of multivariate polynomials ⋮ Recurrence relation associated with the sums of square binomial coefficients ⋮ Creative Telescoping for Holonomic Functions ⋮ On the order of the recurrence produced by the method of creative telescoping

Uses Software

• Maple

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