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Combinatorial polynomials as moments, Hankel transforms, and exponential Riordan arrays. (English) Zbl 1241.11024

It is shown in the case of two combinatorial polynomials that they can exhibited as moments of parametrized families of orthogonal polynomials, and hence derive their Hankel transforms. Exponentials Riordan arrays are the main vehicles used for this.

MSC:

11B83 Special sequences and polynomials
05A15 Exact enumeration problems, generating functions
11C20 Matrices, determinants in number theory
15B05 Toeplitz, Cauchy, and related matrices
15B36 Matrices of integers
42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis

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