Journal of Integer Sequences, Vol. 15 (2012), Article 12.7.2

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

Paul Barry
School of Science
Waterford Institute of Technology


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.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A000111 A000364 A001586 A007405 A039755 A055209 A091804 A147315 A154604.)

Received September 6 2011; revised versions received August 16 2012; September 4 2012. Published in Journal of Integer Sequences, September 8 2012.

Return to Journal of Integer Sequences home page