On the atkin polynomials

Ahmad ElGuindy, Mourad E H Ismail

Research output: Contribution to journalArticle

Abstract

We identify the Atkin polynomials in terms of associated Jacobi polynomials. Our identification then takes advantage of the theory of orthogonal polynomials and their asymptotics to establish many new properties of the Atkin polynomials. This shows that corecursive polynomials may lead to interesting sets of orthogonal polynomials.

Original languageEnglish
Pages (from-to)111-130
Number of pages20
JournalPacific Journal of Mathematics
Volume272
Issue number1
DOIs
Publication statusPublished - 2014

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Keywords

  • Associated Jacobi polynomials
  • Asymptotics
  • Birth and death process polynomials
  • Hecke operators
  • Modular function
  • Scaled invariant
  • Supersingular polynomials
  • Weight functions

ASJC Scopus subject areas

  • Mathematics(all)

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