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Limit Transitions for BC Type Multivariable Orthogonal Polynomials

Published online by Cambridge University Press:  20 November 2018

Jasper V. Stokman  and
Tom H. Koornwinder
Jasper V. Stokman
Affiliation:
Faculty WINS, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands e-mail: jasper@wins.uva.nl, thk@wins.uva.nl
Tom H. Koornwinder
Affiliation:
Faculty WINS, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam, The Netherlands e-mail: jasper@wins.uva.nl, thk@wins.uva.nl
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Abstract

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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.

Keywords

33D4533C50
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 49 , Issue 2 , 01 April 1997 , pp. 374 - 405
Copyright
Copyright © Canadian Mathematical Society 1997

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