A connection between a generalized Pascal matrix and the hypergeometric function
type: Item
instance of: scholarly article
title: A connection between a generalized Pascal matrix and the hypergeometric function
zbMATH Open document ID: 1055.33001
DOI: 10.1016/S0893-9659(03)90123-6
author: Gi-Sang Cheon
author: Moawwad El-Mikkawy
published in: Applied Mathematics Letters
publication date: 2004-06-15T00:00:00Z
review text: The authors consider the generalized Pascal matrix \(P\) and a lower triangular matrix \(L\) defined as follows, \[ [P(t)]_{ij} = {_2F_1} \left[1-i,1-j; 1;\frac{1}{t^2}\right]t^{i+j-2},\qquad [L(t)]_{ij}=\frac{(i-1)!t^{i-j}}{(j-1)!(i-j)!}\,. \] By elementary methods they establish the Cholesky decomposition \(P(t) = L(t)\) \(L{t}^T\). From one of Gauss' relations between contiguous functions, a recurrence relation for \(P(t)\) easily follows; this relation is then used to obtain an algorithm for computing the elements of \(P(t)\).
Mathematics Subject Classification ID: 33C05
Mathematics Subject Classification ID: 15A99
zbMATH DE Number: 2075534
zbMATH Keywords: hypergeometric polynomials
zbMATH Keywords: Cholesky decomposition
zbMATH Keywords: Pascal matrix
zbMATH Keywords: hypergeometric function
reviewed by: Per W. Karlsson
describes a project that uses: Maple
MaRDI profile type: Publication
cites work: Q3844537
cites work: The linear algebra of the Pascal matrix
cites work: Stirling matrix via Pascal matrix
cites work: On solving linear systems of the Pascal type
cites work: The linear algebra of the generalized Pascal matrix
cites work: Q4382605
cites work: Q4382673
full work available at URL: s0893-9659(03)90123-6
OpenAlex ID: W1966608650
description: scientific article; zbMATH DE number 2075534