Results on the associated Jacobi and Gegenbauer polynomials
type: Item
instance of: scholarly article
title: Results on the associated Jacobi and Gegenbauer polynomials
zbMATH Open document ID: 0797.33004
DOI: 10.1016/0377-0427(93)90144-Z
author: Stanisław Lewanowicz
published in: Journal of Computational and Applied Mathematics
publication date: 1994-10-10T00:00:00Z
review text: In this paper the author first proves that the coefficients \(b_{nk}^{(\alpha, \beta)}\) which occur in the expansion of associated Jacobi polynomials \(P_ n^{(\alpha, \beta)} (x;c)\) due to \textit{J. Wimp} [Can. J. Math. 39, 983-1000 (1987; Zbl 0643.33009)] in terms of classical Jacobi polynomials \(P_ n^{(\alpha, \beta)}(x)\) obey a second order recurrence relation which yields the explicit forms for \(b_{nk}^{(\alpha, \beta)}\) in the special cases (i) \(\alpha = \beta\), and (ii) \(\alpha = 1/2\) or \(\beta = 1/2\). The explicit form of \(b_{nk}^{\alpha, \beta)}\) when \(\alpha = \beta\) has been used to give a generalization of the corresponding classical result for associated Gegenbauer polynomials.
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 540458
zbMATH Keywords: associated Jacobi polynomials
zbMATH Keywords: associated Gegenbauer polynomials
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 540458