On the restricted Chebyshev–Boubaker polynomials

Paul Barry

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Using the language of Riordan arrays, we study a one-parameter family of orthogonal polynomials that we call the restricted Chebyshev–Boubaker polynomials. We characterize these polynomials in terms of the three term recurrences that they satisfy, and we study certain central sequences defined by their coefficient arrays. We give an integral representation for their moments, and we show that the Hankel transforms of these moments have a simple form. We show that the (sequence) Hankel transform of the row sums of the corresponding moment matrix is defined by a family of polynomials closely related to the Chebyshev polynomials of the second kind, and that these row sums are in fact the moments of another family of orthogonal polynomials.

Original languageEnglish
Pages (from-to)223-238
Number of pages16
JournalIntegral Transforms and Special Functions
Volume28
Issue number3
DOIs
Publication statusPublished - 04 Mar 2017

Keywords

  • Boubaker polynomials
  • Chebyshev polynomials
  • generating functions
  • orthogonal polynomials
  • Riordan array

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