Generating functions via integral transforms
type: Item
instance of: scholarly article
title: Generating functions via integral transforms
zbMATH Open document ID: 1119.33008
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-04-26T00:00:00Z
review text: Let \(\{P_n\}_{n\geq0}\) be a polynomial sequence with complex coefficients and generated by \[ G(x,t)=\sum_{n=0}^{\infty}P_n(x)t^n. \] Starting from this generating function, the authors find other generating functions of the type: \[ G_\gamma(x,t)=\sum_{n=0}^{\infty}\gamma_n P_n(x)t^n, \] where \(\{\gamma_n\}_{n\geq0}\) is a real number sequence independent on \(x\) and \(t\) and having the integral representation: \[ \gamma_n=\int_{0}^{\infty}t^nd\mu(t),\quad n=0,1,\ldots \] \(\mu\) being a nonnegative measure on \([0,\infty[\). They treat separately the cases where the support is \([a,b]\subset [0,\infty[\) and the case where the support is \([0,\infty[\) with the additional condition: \(\lim_{n\longrightarrow +\infty}{\gamma_{n+1}\over \gamma_n}=+\infty\). It was shown that the derived results in this paper are an unification and a generalization of some known results obtained by Borel, Rainville, McBride and Srivastava. Various explicit examples were considered for illustration.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 41A58
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 5146735
zbMATH Keywords: Generating functions
zbMATH Keywords: Multiplier sequences
zbMATH Keywords: Generalized hypergeometric polynomials
zbMATH Keywords: Basic hypergeometric polynomials
author: Youssèf Ben Cheikh
author: Imed Lamiri
reviewed by: Youssèf Ben Cheikh
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.09.052
OpenAlex ID: W2008919954
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DOI: 10.1016/J.JMAA.2006.09.052
description: scientific article; zbMATH DE number 5146735