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This article is cited in 4 scientific papers (total in 4 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.
Received: March 1, 2011; Published online April 21, 2011
Citation:
Tom H. Koornwinder, “On the Limit from $q$-Racah Polynomials to Big $q$-Jacobi Polynomials”, SIGMA, 7 (2011), 040, 8 pp.
Linking options:
https://www.mathnet.ru/eng/sigma598 https://www.mathnet.ru/eng/sigma/v7/p40
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Abstract page: | 159 | Full-text PDF : | 59 | References: | 35 |
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