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Limit transitions for BC type multivariable orthogonal polynomials |
Canad. J. Math. 49(1997), 373-404
Published:1997-04-01
Printed: Apr 1997
Printed: Apr 1997
- Jasper V. Stokman
- Tom H. Koornwinder
Abstract
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.
| MSC Classifications: |
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 |