Addition theorems via continued fractions
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- by Mourad E. H. Ismail and Jiang Zeng PDF
- Trans. Amer. Math. Soc. 362 (2010), 957-983 Request permission
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.References
Additional Information
- Mourad E. H. Ismail
- Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
- MR Author ID: 91855
- Jiang Zeng
- Affiliation: Université de Lyon, Université Lyon 1, Institute Camille Jordan, UMR 5028 du CNRS, 69622 Villeurbanne, France
- Received by editor(s): August 3, 2007
- Received by editor(s) in revised form: May 5, 2008
- Published electronically: September 10, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2551512