Quadratic transformations for orthogonal polynomials in one and two variables
Copyright policy )Quadratic transformations for orthogonal polynomials in one and two variables
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.
v2: minor corrections, 24 pages
- University of Amsterdam Netherlands
Koornwinder polynomials in two variables, 33C52, 33D45, quadratic transformations, $BC_2$-type Jacobi polynomials, 33D52, 33C45, 004, ($q$-)Askey scheme, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, orthogonal polynomials, 33C45, 33C52, 33D45, 33D52, orthogonal polynomials in two variables
Koornwinder polynomials in two variables, 33C52, 33D45, quadratic transformations, $BC_2$-type Jacobi polynomials, 33D52, 33C45, 004, ($q$-)Askey scheme, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, orthogonal polynomials, 33C45, 33C52, 33D45, 33D52, orthogonal polynomials in two variables
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