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# Limit transitions for BC type multivariable orthogonal polynomials

Published:1997-04-01
Printed: Apr 1997
• Jasper V. Stokman
• Tom H. Koornwinder
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## 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

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