Classical and Semi-Classical Orthogonal Polynomials Defined by Riordan Arrays, and Their Moment Sequences
Paul Barry and Arnauld Mesinga Mwafise
School of Science
Waterford Institute of Technology
We study the orthogonal polynomials of classical and semi-classical
types that can be defined by ordinary and exponential Riordan arrays.
We identify their moment sequences, giving their integral
representations and Hankel transforms. For a special class of classical
orthogonal polynomials defined by Riordan arrays, we identify a complementary family of orthogonal polynomials defined by reversion of moment
sequences. Special product sequences arise and their generating
functions are calculated.
Full version: pdf,
(Concerned with sequences
Received January 18 2017; revised versions received December 29 2017; December 30 2017.
Published in Journal of Integer Sequences, January 21 2018.
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