Inequalities for Legendre functions and Gegenbauer functions
type: Item
instance of: scholarly article
title: Inequalities for Legendre functions and Gegenbauer functions
zbMATH Open document ID: 0731.41020
DOI: 10.1016/0021-9045(91)90077-N
published in: Journal of Approximation Theory
publication date: 1991-01-01T00:00:00Z
review text: The well known inequalities for the Legendre functions of the first kind \(P^{\mu}_{\nu}(x)\), \(\nu\),\(\mu\in N\), \(x\in [-1;1]\), are significantly improved. These inequalities have the disadvantage that the bounds of the Legendre functions tend to infinity as \(x\to 1\). Moreover, two new inequalities for the \(P_{\nu}^{-\mu}(x)\), \(\nu\),\(\mu\in R\), \(\mu >-1/2\), \(\nu\)-\(\mu\geq 2\) and the Gegenbauer functions \(C^{\lambda}_{\alpha}(x)\), \(\alpha\),\(\lambda\in R\), \(\lambda >0\), \(\alpha\geq 2\) are established. In these inequalities the bounds of the special functions are finite on the whole [-1;1].
Mathematics Subject Classification ID: 41A17
zbMATH DE Number: 4208743
zbMATH Keywords: Legendre functions
zbMATH Keywords: Gegenbauer functions
author: Georg Lohöfer
reviewed by: D. K. Ugulava
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4208743