The moment problem associated with the \(q\)-Laguerre polynomials
type: Item
instance of: scholarly article
title: The moment problem associated with the \(q\)-Laguerre polynomials
zbMATH Open document ID: 1018.44008
author: Jacob Stordal Christiansen
published in: Constructive Approximation
publication date: 2003-03-17T00:00:00Z
review text: The indeterminate Stieltjes moment problem associated with the \(q\)-Laguerre polynomials is considered. A transformation of the set of solutions, which has all the classical solutions as fixed points, is established and a method to construct, for example, continuous singular solutions is presented. The connection with the moment problem associated with the Stieltjes-Wigert polynomials is studied. It is shown how to come from \(q\)-Laguerre solutions to Stieltjes-Wigert solutions by letting the parameter \(\alpha \to\infty\). It is also explained how to lift a Stieltjes-Wigert solution to a \(q\)-Laguerre solution at the level of Pick functions. Finally based on two generating functions, expressions for the four entire functions from the Nevanlinna parametrization are obtained.
reviewed by: Som Prakash Goyal
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 33D45
zbMATH DE Number: 1883397
zbMATH Keywords: indeterminate moment problems
zbMATH Keywords: \(q\)-Laguerre polynomials
zbMATH Keywords: Stieltjes-Wigert polynomials
zbMATH Keywords: Nevanlinna parametrization
zbMATH Keywords: indeterminate Stielties moment problem
zbMATH Keywords: continuous singular solutions
zbMATH Keywords: Pick functions
MaRDI profile type: Publication
full work available at URL: s00365-001-0017-5
OpenAlex ID: W2093871154
DOI: 10.1007/S00365-001-0017-5
description: scientific article; zbMATH DE number 1883397