Barry, Paul; Hennessy, Aoife

Meixner-type results for Riordan arrays and associated integer sequences

J. Integer Seq. 13(9), Article 10.9.4, 34 p., electronic only (2010)


Summary: 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.

Mathematics Subject Classification

42C05, 11B83, 33C45, 11B39, 11C20, 15B05, 15B36


Chebyshev polynomials, Boubaker polynomials, integer sequence, orthogonal polynomials, riordan array, production matrix, Hankel determinant, Hankel transform