Inequalities for orthonormal Laguerre polynomials
type: Item
instance of: scholarly article
title: Inequalities for orthonormal Laguerre polynomials
zbMATH Open document ID: 1108.33010
published in: Journal of Approximation Theory
publication date: 2007-02-14T00:00:00Z
review text: The following inequality is established: \[ 10^{-8}<k^{1/6}(k+ \alpha+1)^{-1/2} \max_{x\geq 0}M_k^\alpha(x)<1444(\alpha\geq 24), \] where the upper bound holds for \(k\geq 35\), and lower one for \(k\geq 2 \times 10^{10}\). Also \(M^\alpha_k(x)= (L_k^{(\alpha)}(x))^2e^{-x}x^{\alpha+1}\) and \(L_k^{(\alpha)}(x)\) is an orthonormal polynomial of degree \(k\). Sharp pointwise estimates on \(M_k^\alpha\) and related functions for \(x\geq 0\) are also given.
Mathematics Subject Classification ID: 33C45
zbMATH DE Number: 5125991
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: Laguerre polynomials
author: Ilia Krasikov
reviewed by: Som Prakash Goyal
MaRDI profile type: Publication
full work available at URL: j.jat.2006.04.005
OpenAlex ID: W1990570272
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DOI: 10.1016/J.JAT.2006.04.005
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description: scientific article; zbMATH DE number 5125991