Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A $ q$-beta integral on the unit circle and some biorthogonal rational functions

Authors: Waleed A. Al-Salam and Mourad E. H. Ismail
Journal: Proc. Amer. Math. Soc. 121 (1994), 553-561
MSC: Primary 33D45; Secondary 33D05
MathSciNet review: 1215197
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we first consider a pair of polynomial sets which are biorthogonal on the unit circle with respect to a complex weight function. We then show how the biorthogonality of this pair of polynomial sets implies a q-beta integral which in turn leads to a pair of biorthogonal rational functions. Finally we show that the asymptotics for these pairs of rational functions exhibit qualitative properties reminiscent of the Szegö theory for orthogonal polynomials.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 33D45, 33D05

Retrieve articles in all journals with MSC: 33D45, 33D05

Additional Information

Keywords: Biorthogonal rational functions, q-beta integrals, asymptotics, generating functions, Askey-Wilson integral
Article copyright: © Copyright 1994 American Mathematical Society