Some properties of \(q\)-biorthogonal polynomials
type: Item
instance of: scholarly article
title: Some properties of \(q\)-biorthogonal polynomials
zbMATH Open document ID: 1113.33018
author: Burak Şekeroğlu
author: Fatma Taşdelen
author: H. M. Srivastava
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-02-14T00:00:00Z
review text: \textit{W. A. Al-Salam} and \textit{A. Verma} [Pac. J. Math. 108, 1--7 (1983; Zbl 0471.33009)] constructed some \(q\)-extensions of a pair of biorthogonal polynomials \(Y_n^\alpha(x;k)\) and \(Z^\alpha_n(x;k)\) \((\alpha>-1;k\in N)\), which they called the \(q\)-Konhauser polynomials. \textit{V. K. Jain} and \textit{H. M. Srivastava} [J. Math. Anal. Appl. 166, 331--344 (1992; Zbl 0752.33008)], derived linear and bilinear generating functions for one of these \(q\)-Konhauser polynomials and also suggested an alternative pair of \(q\)-Konhauser biorthonal polynomials. In this paper a systematic investigation of the general family of \(q\)-biorthogonal polynomials is presented and several interesting properties and results are derived for these \(q\)-polynomials.
Mathematics Subject Classification ID: 33D45
zbMATH DE Number: 5125942
zbMATH Keywords: biorthogonal polynomials
zbMATH Keywords: \(q\)-Laguerre polynomials
zbMATH Keywords: \(q\)-biorthogonal polynomials
zbMATH Keywords: \(q\)-Konhauser polynomials
zbMATH Keywords: Rodrigues formulas
zbMATH Keywords: raising operators
reviewed by: Som Prakash Goyal
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.03.046
OpenAlex ID: W2074302585
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DOI: 10.1016/J.JMAA.2006.03.046
description: scientific article; zbMATH DE number 5125942