SIGMA 7 (2011), 040, 8 pages arXiv:1011.5585
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
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.
Askey scheme; q-Askey scheme; q-Racah polynomials; big q-Jacobi polynomials; multi-parameter limit.
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