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Characterizations of continuous and discrete q-ultraspherical polynomials.

Can. J. Math.-J. Can. Math. 63, 181-199 (2011)
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We characterize the continuous q-ultraspherical polynomials in terms of the special form of the coefficients in the expansion DqPn(x) in the basis {Pn(x)}, Dq being the Askey--Wilson divided difference operator. The polynomials are assumed to be symmetric, and the connection coefficients are multiples of the reciprocal of the square of the L2 norm of the polynomials. A similar characterization is given for the discrete q-ultraspherical polynomials. A new proof of the evaluation of the connection coefficients for big q-Jacobi polynomials is given.
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Publikationstyp Artikel: Journalartikel
Dokumenttyp Wissenschaftlicher Artikel
Schlagwörter Continuous q-ultraspherical polynomials; Big q-Jacobi polynomials; Discrete q-ultra-spherical polynomials; Askey--Wilson operator; q-difference operator; Recursion coefficients
ISSN (print) / ISBN 0008-414x
e-ISSN 1496-4279
Quellenangaben Band: 63, Heft: 1, Seiten: 181-199 Artikelnummer: , Supplement: ,
Verlag Canadian Mathematical Society ; University of Toronto Press
Begutachtungsstatus Peer reviewed