Szegö's conjecture on Lebesgue constants for Legendre series
type: Item
instance of: scholarly article
title: Szegö's conjecture on Lebesgue constants for Legendre series
zbMATH Open document ID: 0664.42012
author: C. K. Qu
author: Roderick Wong
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: In 1926, Szegö conjectured that the Lebesgue constants for Legendre series form a monotonically increasing sequence. In this paper, we prove that his conjecture is true. Our method is based on an asymptotic expansion together with an explicit error bound, and makes use of some recent results of Baratella and Gatteschi concerning uniform asymptotic approximations of the Jacobi polynomials.
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 4086263
zbMATH Keywords: Lebesgue constants for Legendre series
zbMATH Keywords: error bound
zbMATH Keywords: uniform asymptotic approximations of the Jacobi polynomials
MaRDI profile type: Publication
full work available at URL: pjm.1988.135.157
OpenAlex ID: W2066525467
Wikidata QID: Q123182059
DOI: 10.2140/PJM.1988.135.157
description: scientific article; zbMATH DE number 4086263