Journal of Integer Sequences, Vol. 13 (2010), Article 10.9.4

Meixner-Type Results for Riordan Arrays and Associated Integer Sequences

Paul Barry
School of Science
Waterford Institute of Technology

Aoife Hennessy
Department of Computing, Mathematics and Physics
Waterford Institute of Technology


We determine which (ordinary) Riordan arrays are the coefficient arrays of a family of orthogonal polynomials. In so doing, we are led to introduce a family of polynomials, which includes the Boubaker polynomials, and a scaled version of the Chebyshev polynomials, using the techniques of Riordan arrays. We classify these polynomials in terms of the Chebyshev polynomials of the first and second kinds. We also examine the Hankel transforms of sequences associated with the inverse of the polynomial coefficient arrays, including the associated moment sequences.

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(Concerned with sequences A000007 A000045 A000108 A001405 A007318 A009766 A033184 A049310 A053117 A053120 A053121 A098615 A108044 A108045 A131386.)

Received May 14 2010; revised version revised version received September 8 2010; October 4 2010. Published in Journal of Integer Sequences, December 6 2010.

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