An extension of Zeilberger's fast algorithm to general holonomic functions
type: Item
instance of: scholarly article
title: An extension of Zeilberger's fast algorithm to general holonomic functions
zbMATH Open document ID: 0968.33011
DOI: 10.1016/S0012-365X(99)00259-9
author: Frédéric Chyzak
published in: Discrete Mathematics
publication date: 2001-09-12T00:00:00Z
review text: In this work, an algorithm is given for the summation of holomonic sequences, therefore generalizing Zeilberger's algorithm which works for hypergeometric sequences. Whereas Zeilberger's approach is a clever application of Gosper's algorithm, in the current paper an algorithm of Abramov for the computation of rational solutions of recurrence equations with polynomial coefficients is used. With this approach, identities like \[ \sum_{k=0}^n\Biggl(\sum_{j=0}^k{n \choose j}\Biggr)^3= n2^{3n-1}+2^{3n}-3n2^{n-2} {2n \choose n} \] can be computer-generated. The technique can be extended to the differential case and to \(q\)-calculus.
reviewed by: W. Koepf
Mathematics Subject Classification ID: 33F10
Mathematics Subject Classification ID: 68W30
Mathematics Subject Classification ID: 05A19
zbMATH DE Number: 1453348
zbMATH Keywords: \(\partial\)-finite functions
zbMATH Keywords: D-finite functions
zbMATH Keywords: holonomic functions
zbMATH Keywords: symbolic integration
zbMATH Keywords: symbolic summation
zbMATH Keywords: Zeilberger's algorithm
zbMATH Keywords: Gosper's algorithm
zbMATH Keywords: hypergeometric sequences
zbMATH Keywords: Abramov's algorithm
describes a project that uses: qZeil
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1453348