Some identities on Catalan numbers and hypergeometric functions via Catalan matrix power
type: Item
instance of: scholarly article
title: Some identities on Catalan numbers and hypergeometric functions via Catalan matrix power
zbMATH Open document ID: 1222.15035
author: Stefan Stanimirović
published in: Applied Mathematics and Computation
publication date: 2011-06-27T00:00:00Z
review text: The author defines the Pascal matrix \(P_{n}(x)\) to be the \(n\times n\) upper triangular matrix whose \((i,j)\)th entry is \(x^{i-j}\binom{i-1}{j-1}\) and the Catalan matrix \(C_{n}(x)\) as the \(n\times n\) triangular matrix whose \((i,j)\)th entry is \(x^{i-j}\frac{1}{i-j+1}\binom{2i-2j}{i-j}\). He then defines \(G_{n}(x):=C_{n}(x)^{-1}P_{n}(x)\) where the entries of \(G_{n}(x)\) can be described explicitly in terms of the binomial coefficients and the hypergeometric function \(_{2}F_{1}\). Using various products of these matrices the author derives a series of identities involving the Catalan numbers and values of \(_{2}F_{1}\) and \(_{3}F_{2}\).
reviewed by: John D. Dixon
Mathematics Subject Classification ID: 15B36
Mathematics Subject Classification ID: 05A10
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 15A24
zbMATH DE Number: 5913724
zbMATH Keywords: Catalan number
zbMATH Keywords: binomial coefficient
zbMATH Keywords: hypergeometric function
zbMATH Keywords: Catalan matrix
zbMATH Keywords: Pascal matrix
zbMATH Keywords: identities
zbMATH Keywords: \(_{2}F_{1}\)
zbMATH Keywords: \(_{3}F_{2}\).
describes a project that uses: SumTools
MaRDI profile type: Publication
full work available at URL: j.amc.2011.03.138
OpenAlex ID: W2059931381
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DOI: 10.1016/J.AMC.2011.03.138
description: scientific article; zbMATH DE number 5913724