A note on the Koekoeks' differential equation for generalized Jacobi polynomials
type: Item
instance of: scholarly article
title: A note on the Koekoeks' differential equation for generalized Jacobi polynomials
zbMATH Open document ID: 0945.33005
DOI: 10.1016/S0377-0427(99)00180-6
author: H. Bavinck
published in: Journal of Computational and Applied Mathematics
publication date: 2000-10-03T00:00:00Z
review text: For \(\alpha,\beta > -1\) and \(M,N \geq 0\), let \(\{ P_n^{\alpha,\beta,M,N}(x) \}_{n=0}^{\infty}\) be the polynomials orthogonal on \([-1,1]\) with respect to \[ {\Gamma(\alpha+\beta+2) \over 2^{\alpha + \beta + 1} \Gamma(\alpha+1) \Gamma(\beta+1)} (1-x)^{\alpha} (1+x)^{\beta} + M\delta (x+1) + N \delta(x-1). \] The author gives simple and direct proofs of the result of J. Koekoek and R. Koekoek that these polynomials satisfy a specific differential equation of finite order provided \(\alpha\) is a nonnegative integer when \(N >0\) and \(\beta\) is a nonnegative integer when \(M>0\).
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 34A35
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 1423310
Wikidata QID: Q115338981
reviewed by: David M. Bressoud
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1423310