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

Barry, Paul (2012) A Note on Three Families of Orthogonal Polynomials defined by Circular Functions, and Their Moment Sequences. Journal of Integer Sequences, 15. ISSN 1530-7638

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Official URL: https://cs.uwaterloo.ca/journals/JIS/

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.

Item Type: Article
Departments or Groups: *NONE OF THESE*
Divisions: School of Science
Depositing User: Paul Barry
Date Deposited: 19 Nov 2012 15:46
Last Modified: 22 Aug 2016 10:26
URI: http://repository.wit.ie/id/eprint/2108

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