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

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....

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Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Main Author: Tom H. Koornwinder
Format: Article
Language:English
Published: National Academy of Science of Ukraine 2011-04-01
Subjects:
Askey scheme
q-Askey scheme
q-Racah polynomials
big q-Jacobi polynomials
multi-parameter limit
Online Access:http://dx.doi.org/10.3842/SIGMA.2011.040
Description
Summary: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.
ISSN:1815-0659

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