
SIGMA 7 (2011), 040, 8 pages arXiv:1011.5585
https://doi.org/10.3842/SIGMA.2011.040
Contribution to the Special Issue “Symmetry, Separation, Superintegrability and Special Functions (S^{4})”
On the Limit from qRacah Polynomials to Big qJacobi Polynomials
Tom H. Koornwinder
Kortewegde 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 qRacah polynomials to big qJacobi polynomials
is given which can be considered as a limit formula for orthogonal polynomials.
This is extended to a multiparameter limit with 3 parameters, also
involving (q)Hahn polynomials, little qJacobi polynomials and
Jacobi polynomials. Also the limits from AskeyWilson to Wilson polynomials
and from qRacah to Racah polynomials are given in a more conceptual way.
Key words:
Askey scheme; qAskey scheme; qRacah polynomials; big qJacobi polynomials; multiparameter limit.
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