Inequalities for the associated Legendre functions
type: Item
instance of: scholarly article
title: Inequalities for the associated Legendre functions
zbMATH Open document ID: 0923.33002
published in: Journal of Approximation Theory
publication date: 1999-06-10T00:00:00Z
review text: The main results are about the bound for the associated Legendre functions of the first kind \(P_n^m(x)\) with fixed \(x\in [-1,1]\) and integer \(m,n,1\leq | m| \leq n.\) First of all, the author proves a result about transferring upper bounds of the Legendre polynomials \(P_n(x)\) to the functions \(P_n^m(x).\) That result allows to obtain bounds of the type \[ A(\alpha ,n,m)\leq \max _{x\in [-1,1]} | (1-x^2)^{\alpha/2}P_n^m(x)| \leq B(\alpha ,n,m) \] for all \(0\leq \alpha \leq 1/2\) and \(1\leq | m| \leq n.\) For \(\alpha =0\) and \(\alpha =1/2\) these upper bounds are improvements and simplifications of known results.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 1297475
zbMATH Keywords: associated Legendre functions
zbMATH Keywords: inequalities
author: Georg Lohöfer
reviewed by: Alexei Lukashov
MaRDI profile type: Publication
full work available at URL: jath.1998.3207
OpenAlex ID: W2063575337
cites work: Q3918407
cites work: An inequality for Legendre polynomials
cites work: Inequalities for ultraspherical polynomials and application to quadrature
cites work: Q3766072
cites work: Q4275389
cites work: Inequalities for Legendre functions and Gegenbauer functions
cites work: Alternative Proof of a Sharpened Form of Bernstein's Inequality for Legendre Polynomials
cites work: Q5518575
cites work: Unitarity and High-Energy Behavior of Scattering Amplitudes
cites work: Q4853626
cites work: Q4843476
cites work: Analytic Inequalities
cites work: Q4059363
DOI: 10.1006/JATH.1998.3207
description: scientific article; zbMATH DE number 1297475