Journal of Integer Sequences, Vol. 21 (2018), Article 18.1.5

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.

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(Concerned with sequences A000045 A000108 A000984 A001045 A001147 A049027 A059304 A081696 A098614 A200375.)

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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