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A Characterization of the Continuous q-Ultraspherical Polynomials

Published online by Cambridge University Press:  20 November 2018

Waleed Al-Salam ,
WM. R. Allaway  and
Richard Askey
Waleed Al-Salam
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, CanadaT6G2G1.
WM. R. Allaway
Affiliation:
Department of Mathematical Sciences, Lakehead University, Thunder Bay, Ontario, CanadaP7B5E1.
Richard Askey
Affiliation:
Department of Mathematics, Van Vleck Hall, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin, U.S.A.53706.
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Abstract

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In his Ph.D. thesis Allaway found all polynomials that can be represented as

and a0bn≠0. We solve the essentially equivalent problem of finding all symmetric polynomials with when are orthogonal with respect to dα(x). The polynomials are the continuous q-ultraspherical polynomials and some of their limiting cases.

Keywords

33A6542A52
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 27 , Issue 3 , 01 September 1984 , pp. 329 - 336
Copyright
Copyright © Canadian Mathematical Society 1984

References

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