Journal of Integer Sequences, Vol. 14 (2011), Article 11.2.2

Riordan Arrays, Orthogonal Polynomials as Moments, and Hankel Transforms

Paul Barry
School of Science
Waterford Institute of Technology


Taking the examples of Legendre and Hermite orthogonal polynomi als, we show how to interpret the fact that these orthogonal polynomials are moments of other orthogonal polynomials in terms of t heir associated Riordan arrays. We use these means to calculate the Hankel transforms of the associated polynomial sequences.

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(Concerned with sequences A000007 A000045 A000108 A000262 A001405 A001497 A007318 A009766 A021009 A033184 A053121 A066325 A094587 A094816 A111596 A111884 A119467 A119879 A155585.)

Received May 14 2010; revised version received December 6 2010; January 31 2011. Published in Journal of Integer Sequences, February 19 2011.

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