Approximation of the Jacobi polynomials and the Racah coefficients
type: Item
instance of: scholarly article
title: Approximation of the Jacobi polynomials and the Racah coefficients
zbMATH Open document ID: 1196.41020
DOI: 10.1216/RMJ-2010-40-3-849
published in: Rocky Mountain Journal of Mathematics
publication date: 2010-07-23T00:00:00Z
review text: This paper is a continuation of the studies of the authors in [Rocky Mt. J. Math. 37, No.1, 159--184 (2007; Zbl 1193.33024)] which provides extensions of the earlier obtained results to a subinterval of the interval of orthogonality \((-1,1)\) of the Jacobi polynomials \(P_{n}^{(\alpha, \beta)}(x)\). More specifically, the authors obtain asymptotic approximations to the Jacobi polynomials \(P_{n}^{(\alpha, \beta)}(x)\) and to the Racah coefficients \(P_{n}^{(an+c, bn+d)}(x)\), as \(n\rightarrow \infty\), where \(a,b,c,d\) are constants. The approximations to \(P_{n}^{(\alpha, \beta)}(x)\) are generated by the construction of certain fundamental sets of solutions to a hypergeometric differential equation.
reviewed by: Stamatis Koumandos
Mathematics Subject Classification ID: 41A60
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 34E10
zbMATH DE Number: 5760097
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: hypergeometric differential equation
zbMATH Keywords: asymptotic approximations
author: U. Elias
author: H. Gingold
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5760097