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VOL. 76 | 2018 Quadratic transformations for orthogonal polynomials in one and two variables
Tom H. Koornwinder

Editor(s) Hitoshi Konno, Hidetaka Sakai, Junichi Shiraishi, Takao Suzuki, Yasuhiko Yamada

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.

Information

Published: 1 January 2018
First available in Project Euclid: 21 September 2018

zbMATH: 07039309
MathSciNet: MR3837928

Digital Object Identifier: 10.2969/aspm/07610419

Subjects:
Primary: 33C45, 33C52, ‎33D45, 33D52

Rights: Copyright © 2018 Mathematical Society of Japan

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