A Note on Three Families of Orthogonal Polynomials defined by Circular Functions, and Their Moment Sequences
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,
(Concerned with sequences
Received September 6 2011;
revised versions received August 16 2012; September 4 2012.
Published in Journal of Integer Sequences, September 8 2012.
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