Limit transitions for BC type multivariable orthogonal polynomials
Printed: Apr 1997
Jasper V. Stokman
Tom H. Koornwinder
Limit transitions will be derived between the five parameter
family of Askey-Wilson polynomials, the four parameter family of
big $q$-Jacobi polynomials and the three parameter family of little
$q$-Jacobi polynomials in $n$ variables associated with root system $\BC$.
These limit transitions generalize the known hierarchy structure between
these families in the one variable case. Furthermore it will be proved
that these three families are $q$-analogues of the three parameter
family of $\BC$ type Jacobi polynomials in $n$ variables. The limit
transitions will be derived by taking limits of $q$-difference operators
which have these polynomials as eigenfunctions.
33D45 - Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
33C50 - Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable