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A q-Beta Integral on the Unit Circle and Some Biorthogonal Rational Functions
Waleed A. Al-Salam and Mourad E. H. Ismail
Proceedings of the American Mathematical Society
Vol. 121, No. 2 (Jun., 1994), pp. 553-561
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2160434
Page Count: 9
You can always find the topics here!Topics: Polynomials, Mathematical integrals, Rational functions, Weighting functions, Mathematical functions, Recurrence relations
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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.
Proceedings of the American Mathematical Society © 1994 American Mathematical Society