Meixner-type results for Riordan arrays and associated integer sequences

Paul Barry, Aoife Hennessy

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)

Abstract

We determine which (ordinary) Riordan arrays are the coefficient arrays of a family of orthogonal polynomials. In so doing, we are led to introduce a family of polynomi- als, which includes the Boubaker polynomials, and a scaled version of the Chebyshev polynomials, using the techniques of Riordan arrays. We classify these polynomials in terms of the Chebyshev polynomials of the first and second kinds. We also exam- ine the Hankel transforms of sequences associated with the inverse of the polynomial coefficient arrays, including the associated moment sequences.

Original languageEnglish
Pages (from-to)1-34
Number of pages34
JournalJournal of Integer Sequences
Volume13
Issue number9
Publication statusPublished - 2010

Keywords

  • Boubaker polynomials
  • Chebyshev polynomials
  • Hankel determinant
  • Hankel transform
  • Integer sequence
  • Orthogonal polynomials
  • Production matrix
  • Riordan array

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