Weighted L2-norms of Gegenbauer polynomials

Johann Brauchart; Peter Grabner

doi:10.1007/s00010-022-00871-9

Weighted L2-norms of Gegenbauer polynomials

Johann Brauchart, Peter Grabner

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article

Abstract

We study integrals of the form ∫-11(Cn(λ)(x))2(1-x)α(1+x)βdx,where Cn(λ) denotes the Gegenbauer-polynomial of index λ> 0 and α, β> - 1. We give exact formulas for the integrals and their generating functions, and obtain asymptotic formulas as n→ ∞.

Original language	English
Pages (from-to)	741-762
Number of pages	22
Journal	Aequationes Mathematicae
Volume	96
Issue number	4
DOIs	https://doi.org/10.1007/s00010-022-00871-9
Publication status	Published - Aug 2022

Keywords

Asymptotic analysis
Gegenbauer polynomials
Hypergeometric functions

ASJC Scopus subject areas

Applied Mathematics
Mathematics(all)
Discrete Mathematics and Combinatorics

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10.1007/s00010-022-00871-9

https://arxiv.org/pdf/2103.08303.pdfLicence: CC BY 4.0

Cite this

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AB - We study integrals of the form ∫-11(Cn(λ)(x))2(1-x)α(1+x)βdx,where Cn(λ) denotes the Gegenbauer-polynomial of index λ> 0 and α, β> - 1. We give exact formulas for the integrals and their generating functions, and obtain asymptotic formulas as n→ ∞.

KW - Asymptotic analysis

KW - Gegenbauer polynomials

KW - Hypergeometric functions

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Weighted L2-norms of Gegenbauer polynomials

Abstract

Keywords

ASJC Scopus subject areas

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