arXiv Analytics

Sign in

arXiv:1011.5585 [math.CA]AbstractReferencesReviewsResources

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

Tom H. Koornwinder

Published 2010-11-25, updated 2011-11-04Version 4

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.

Comments: dedicated to Willard Miller on the occasion of his retirement; the unnumbered formula after (2.5) is corrected
Journal: SIGMA 7 (2011), 040, 8 pages
Categories: math.CA
Subjects: 33D45, 33C45
Related articles: Most relevant | Search more
arXiv:1011.1429 [math.CA] (Published 2010-11-05, updated 2010-11-25)
A limit $q=-1$ for the big q-Jacobi polynomials
arXiv:math/0403159 [math.CA] (Published 2004-03-09)
On discrete q-ultraspherical polynomials and their duals
arXiv:math/0701345 [math.CA] (Published 2007-01-12)
Irrationality proof of certain Lambert series using little q-Jacobi polynomials

Links

Toolbox