Classical and semi-classical orthogonal polynomials defined by riordan arrays, and their moment sequences

Paul Barry, Arnauld Mesinga Mwafise

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We study the orthogonal polynomials of classical and semi-classical types that can be defined by ordinary and exponential Riordan arrays. We identify their moment sequences, giving their integral representations and Hankel transforms. For a special class of classical orthogonal polynomials defined by Riordan arrays, we identify a complementary family of orthogonal polynomials defined by reversion of moment sequences. Special product sequences arise and their generating functions are calculated.

Original languageEnglish
Pages (from-to)1-40
Number of pages40
JournalJournal of Integer Sequences
Volume21
Issue number1
Publication statusPublished - 20 Dec 2017

Keywords

  • Bessel polynomial
  • Chebyshev polynomial
  • Classical orthogonal polynomial
  • Moment sequence
  • Riordan array

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