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Riordan arrays, orthogonal polynomials as moments, and Hankel transforms. (English) Zbl 1213.42086

Summary: Taking the examples of Legendre and Hermite orthogonal polynomials, we show how to interpret the fact that these orthogonal polynomials are moments of other orthogonal polynomials in terms of their associated Riordan arrays. We use these means to calculate the Hankel transforms of the associated polynomial 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.)
11C20 Matrices, determinants in number theory
15B36 Matrices of integers

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