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arXiv · 1512.09294

Quadratic transformations for orthogonal polynomials in one and two variables

Tom H. Koornwinder
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Abstract

We discuss quadratic transformations for orthogonal polynomials in one and two variables. In the one-variable case we list many (or all) quadratic transformations between families in the Askey scheme or $q$-Askey scheme. In the two-variable case we focus, after some generalities, on the polynomials associated with root system $BC_2$, i.e., $BC_2$-type Jacobi polynomials if $q=1$ and Koornwinder polynomials in two variables in the $q$-case.

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Tom H. Koornwinder. 2018-07-18. Quadratic transformations for orthogonal polynomials in one and two variables. https://arxiv.org/abs/1512.09294

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