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Meixner-type results for Riordan arrays and associated integer sequences. (English) Zbl 1201.42017

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.

MSC:

42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis
11B83 Special sequences and polynomials
33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
11B39 Fibonacci and Lucas numbers and polynomials and generalizations
11C20 Matrices, determinants in number theory
15B05 Toeplitz, Cauchy, and related matrices
15B36 Matrices of integers

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