Transactions of the American Mathematical Society

Author(s): Mourad E. H. Ismail; Jiang Zeng
Journal: Trans. Amer. Math. Soc. 362 (2010), 957-983.
MSC (2000): Primary 33D15, 33C15; Secondary 30E05, 05A15
Posted: September 10, 2009
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 33D15, 33C15, 30E05, 05A15

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: 10.1090/S0002-9947-09-04868-5
PII: S 0002-9947(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
Posted: September 10, 2009
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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