Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 7 (2011), 040, 8 pages      arXiv:1011.5585      http://dx.doi.org/10.3842/SIGMA.2011.040
Contribution to the Special Issue “Symmetry, Separation, Super-integrability and Special Functions (S4)”

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

Received March 01, 2011; Published online April 21, 2011

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.

Key words: Askey scheme; q-Askey scheme; q-Racah polynomials; big q-Jacobi polynomials; multi-parameter limit.

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References

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