A Note on Three Families of Orthogonal Polynomials defined by Circular Functions, and Their Moment Sequences

Paul Barry

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    Using the language of exponential Riordan arrays, we study three distinct families of orthogonal polynomials defined by trigonometric functions. We study the moment sequences of theses families, finding continued fraction expressions for their generating functions, and calculate the Hankel transforms of these moment sequences. Results related to the Euler or zigzag numbers, as well as the generalized Euler or Springer numbers, are found. In addition, we characterize the Dowling numbers as moments of a family of orthogonal polynomials.
    Original languageEnglish
    JournalJournal of Integer Sequences
    Volume15
    Issue number7
    Publication statusPublished - 08 Sep 2012

    Keywords

    • Dowling numbers
    • Euler numbers
    • Exponential Riordan array
    • Hankel transform
    • Moments
    • Orthogonal polynomials

    Fingerprint

    Dive into the research topics of 'A Note on Three Families of Orthogonal Polynomials defined by Circular Functions, and Their Moment Sequences'. Together they form a unique fingerprint.

    Cite this