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

 

Quadratic $q$-exponentials
and connection coefficient problems


Authors: Mourad E. H. Ismail, Mizan Rahman and Dennis Stanton
Journal: Proc. Amer. Math. Soc. 127 (1999), 2931-2941
MSC (1991): Primary 33D45; Secondary 42C15
Published electronically: April 23, 1999
MathSciNet review: 1621949
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Abstract | References | Similar Articles | Additional Information

Abstract: We establish expansion formulas of $q$-exponential functions in terms of continuous $q$-ultraspherical polynomials, continuous $q$-Hermite polynomials and Askey-Wilson polynomials. The proofs are based on solving connection coefficient problems.


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Additional Information

Mourad E. H. Ismail
Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
Email: ismail@math.nsf.edu

Mizan Rahman
Affiliation: Department of Mathematics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: mrahman@math.carleton.ca

Dennis Stanton
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: stanton@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05017-0
PII: S 0002-9939(99)05017-0
Keywords: Askey-Wilson polynomials, continuous $q$-ultraspherical polynomials, $q$-exponential functions, $q$-Bessel functions
Received by editor(s): December 29, 1997
Published electronically: April 23, 1999
Additional Notes: The first author was partially supported by NSF grant DMS-9625459, the second author was partially supported by NSERC grant A6197, and the third author was partially supported by NSF grant DMS-9400510.
Communicated by: Hal. L. Smith
Article copyright: © Copyright 1999 American Mathematical Society