Quadratic -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

DOI:
https://doi.org/10.1090/S0002-9939-99-05017-0

Published electronically:
April 23, 1999

MathSciNet review:
1621949

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Abstract | References | Similar Articles | Additional Information

Abstract: We establish expansion formulas of -exponential functions in terms of continuous -ultraspherical polynomials, continuous -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:
https://doi.org/10.1090/S0002-9939-99-05017-0

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