Riordan arrays, orthogonal polynomials as moments, and Hankel transforms

By Paul Barry. 2011

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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.

Subfields: Applied Mathematics, Computational Mechanics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/16f9e6e57bf00b4a199bb986b1c9623a41092612