Quadratic transformations for orthogonal polynomials in one and two variables
Classical Analysis and ODEs
2018-07-19 v2
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 -Askey scheme. In the two-variable case we focus, after some generalities, on the polynomials associated with root system , i.e., -type Jacobi polynomials if and Koornwinder polynomials in two variables in the -case.
Cite
@article{arxiv.1512.09294,
title = {Quadratic transformations for orthogonal polynomials in one and two variables},
author = {Tom H. Koornwinder},
journal= {arXiv preprint arXiv:1512.09294},
year = {2018}
}
Comments
v2: minor corrections, 24 pages