Asymptotics and weighted estimates of Meixner polynomials orthogonal on the grid \(\{ 0,\delta,2\delta,\dots\}\)
type: Item
instance of: scholarly article
title: Asymptotics and weighted estimates of Meixner polynomials orthogonal on the grid \(\{ 0,\delta,2\delta,\dots\}\)
zbMATH Open document ID: 0919.33011
DOI: 10.1007/BF02358983
author: I. I. Sharapudinov
published in: Mathematical Notes
publication date: 1999-08-26T00:00:00Z
review text: Meixner polynomials are the discrete analogues to Laguerre orthogonal polynomials. The author proves for Meixner polynomials an asymptotic formula in terms of Laguerre polynomials. The proof uses Euler summation formula and an author's estimate for Stirling numbers [\textit{I. I. Sharapudinov}, Math. Sb. 180, No. 9, 1259-1277 (1989; Zbl 0689.33005)]. As a consequence, the author obtains a weighted estimate for the Meixner polynomials on \([0,+\infty[\) by means of a classical estimate for Laguerre polynomials [\textit{R. Askey} and \textit{S. Wainger}, Am. J. Math. 87, 695-708 (1965; Zbl 0125.31301)].
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 1257144
zbMATH Keywords: Meixner polynomials
zbMATH Keywords: Laguerre polynomials
zbMATH Keywords: Stirling numbers
reviewed by: Daniel Duverney
MaRDI profile type: Publication
cites work: Q5519244
cites work: Q3478707
cites work: Q4039375
cites work: Mean Convergence of Expansions in Laguerre and Hermite Series
cites work: Mean Convergence of Hermite and Laguerre Series. I
cites work: Q3031263
full work available at URL: https://doi.org/10.1007/bf02358983
OpenAlex ID: W2081221835
description: scientific article; zbMATH DE number 1257144