If you need an accessible version of this item please contact JSTOR User Support

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
DOI: 10.2307/2160434
Stable URL: http://www.jstor.org/stable/2160434
Page Count: 9
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
A q-Beta Integral on the Unit Circle and Some Biorthogonal Rational Functions
Preview not available

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.

Page Thumbnails

  • Thumbnail: Page 
553
    553
  • Thumbnail: Page 
554
    554
  • Thumbnail: Page 
555
    555
  • Thumbnail: Page 
556
    556
  • Thumbnail: Page 
557
    557
  • Thumbnail: Page 
558
    558
  • Thumbnail: Page 
559
    559
  • Thumbnail: Page 
560
    560
  • Thumbnail: Page 
561
    561