Some questions concerning computer-generated proofs of a binomial double- sum identity
type: Item
instance of: scholarly article
title: Some questions concerning computer-generated proofs of a binomial double- sum identity
zbMATH Open document ID: 0836.05003
author: George E. Andrews
author: Peter Paule
published in: Journal of Symbolic Computation
publication date: 1996-02-20T00:00:00Z
review text: In 1990 D. Zeilberger asked for a computer-generated proof of the following identity: \[ \sum^n_{i = 0} \sum^n_{j = 0} {i + j \choose j}^2 {4n - 2i - 2j \choose 2n - 2j} = (2n + 1) {2n \choose n}^2. \] The authors give two different proofs. The human part of the first proof consists in using a somehow tricky generating function argument. The rest is done by Zeilberger's algorithm in the implementation of \textit{D. Zeilberger} himself for Maple [SIGSAM Bull. 25, 4-13 (1991)] or in that of \textit{P. Paule} and \textit{M. Schorn} for Mathematica (to appear). The second proof is by observing that a generalization of the left hand side of the above formula satisfies a simple structured recurrence relation. This generalization was obtained by an heuristic process using any computer-algebra package. The authors remark that hypergeometric methods seemingly do not succeed.
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 627597
zbMATH Keywords: binomial double-sum identity
zbMATH Keywords: generating function
zbMATH Keywords: Zeilberger's algorithm
reviewed by: Bernd Richter
describes a project that uses: Maple
describes a project that uses: Mathematica
MaRDI profile type: Publication
OpenAlex ID: W1997229336
DOI: 10.1006/JSCO.1993.1038
description: scientific article; zbMATH DE number 627597