Inequalities for ultraspherical polynomials and the gamma function
type: Item
instance of: scholarly article
title: Inequalities for ultraspherical polynomials and the gamma function
zbMATH Open document ID: 0532.33007
DOI: 10.1016/0021-9045(84)90020-0
author: Lee Lorch
published in: Journal of Approximation Theory
publication date: 1984-01-01T00:00:00Z
review text: Der Verf. beweißt mit elementaren Mitteln für die Gegenbauerschen Polynome \(P_ n^{(\lambda)}\) die Abschätzung \[ (\sin \theta)^{\lambda}| P_ n^{(\lambda)}(\cos \theta)|<2^{1- \lambda}/\Gamma(\lambda)(n+\lambda)^{1-\lambda}, \] \[ 0\leq \theta \leq \pi,\quad 0<\lambda<1,\quad n\in N. \] Diese Abschätzung ist besser als \textit{G. Szegö's} Ungleichung [Orthogonal polynomials (1959; Zbl 0089.275)], wo \(n^{1-\lambda}\) statt \((n+\lambda)^{1-\lambda}\) steht. Einige Abschätzungen für \(\Gamma(n+\lambda)/\Gamma(n+1)\) werden betrachtet.
Mathematics Subject Classification ID: 33C55
Mathematics Subject Classification ID: 33B15
zbMATH DE Number: 3844138
MaRDI profile type: Publication
full work available at URL: 0021-9045(84)90020-0
OpenAlex ID: W2068735245
cites work: Q3918407
cites work: Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function
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cites work: Q5339472
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description: scientific article; zbMATH DE number 3844138