English

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 qq-Askey scheme. In the two-variable case we focus, after some generalities, on the polynomials associated with root system BC2BC_2, i.e., BC2BC_2-type Jacobi polynomials if q=1q=1 and Koornwinder polynomials in two variables in the qq-case.

Keywords

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

R2 v1 2026-06-22T12:20:54.822Z