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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Szegő polynomials from hypergeometric functions


Author: A. Sri Ranga
Journal: Proc. Amer. Math. Soc. 138 (2010), 4259-4270
MSC (2010): Primary 33C05, 42C05; Secondary 33C45
Published electronically: July 30, 2010
MathSciNet review: 2680052
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Abstract: Szegő polynomials with respect to the weight function $ \omega(\theta) = e^{\eta \theta} [\sin(\theta/2)]^{2\lambda}$, where $ \eta, \lambda \in \mathbb{R}$ and $ \lambda > -1/2$ are considered. Many of the basic relations associated with these polynomials are given explicitly. Two sequences of para-orthogonal polynomials with explicit relations are also given.


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Additional Information

A. Sri Ranga
Affiliation: Departamento de Ciências de Computao e Estatística, Ibilce, Universidade Estadual Paulista, 15054-000, São José do Rio Preto, SP, Brazil
Email: ranga@ibilce.unesp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10592-0
PII: S 0002-9939(2010)10592-0
Keywords: Hypergeometric function, continued fractions, Szegő polynomials
Received by editor(s): May 14, 2009
Received by editor(s) in revised form: November 3, 2009
Published electronically: July 30, 2010
Communicated by: Peter A. Clarkson
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.