This article is cited in 5 papers

On the Limit from $q$-Racah Polynomials to Big $q$-Jacobi Polynomials

Tom H. Koornwinder

Korteweg--de Vries Institute, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands

Abstract: A limit formula from $q$-Racah polynomials to big $q$-Jacobi polynomials is given which can be considered as a limit formula for orthogonal polynomials. This is extended to a multi-parameter limit with 3 parameters, also involving ($q$-)Hahn polynomials, little $q$-Jacobi polynomials and Jacobi polynomials. Also the limits from Askey–Wilson to Wilson polynomials and from $q$-Racah to Racah polynomials are given in a more conceptual way.

Keywords: Askey scheme; $q$-Askey scheme; $q$-Racah polynomials; big $q$-Jacobi polynomials; multi-parameter limit.

MSC: 33D45; 33C45

Received: March 1, 2011; Published online April 21, 2011

Language: English

DOI: 10.3842/SIGMA.2011.040

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ArXiv: 1011.5585