Weighted L2-norms of Gegenbauer polynomials

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)741-762
Number of pages22
JournalAequationes Mathematicae
Volume96
Issue number4
DOIs
Publication statusPublished - Aug 2022

Keywords

  • Asymptotic analysis
  • Gegenbauer polynomials
  • Hypergeometric functions

ASJC Scopus subject areas

  • Applied Mathematics
  • General Mathematics
  • Discrete Mathematics and Combinatorics

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