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Addition theorems via continued fractions


Authors: Mourad E. H. Ismail and Jiang Zeng
Journal: Trans. Amer. Math. Soc. 362 (2010), 957-983
MSC (2000): Primary 33D15, 33C15; Secondary 30E05, 05A15
DOI: https://doi.org/10.1090/S0002-9947-09-04868-5
Published electronically: September 10, 2009
MathSciNet review: 2551512
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Abstract | References | Similar Articles | Additional Information

Abstract: We show connections between a special type of addition formulas and a theorem of Stieltjes and Rogers. We use different techniques to derive the desirable addition formulas. We apply our approach to derive special addition theorems for Bessel functions and confluent hypergeometric functions. We also derive several addition theorems for basic hypergeometric functions. Applications to the evaluation of Hankel determinants are also given.


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Additional Information

Mourad E. H. Ismail
Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816

Jiang Zeng
Affiliation: Université de Lyon, Université Lyon 1, Institute Camille Jordan, UMR 5028 du CNRS, 69622 Villeurbanne, France

DOI: https://doi.org/10.1090/S0002-9947-09-04868-5
Keywords: Addition theorems, orthogonal polynomials, continued $J$-fractions, $q$-orthogonal polynomials, Askey-Wilson polynomials, Bessel and confluent hypergeometric functions
Received by editor(s): August 3, 2007
Received by editor(s) in revised form: May 5, 2008
Published electronically: September 10, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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