Quadratic exponentials and connection coefficient problems
Authors:
Mourad E. H. Ismail, Mizan Rahman and Dennis Stanton
Journal:
Proc. Amer. Math. Soc. 127 (1999), 29312941
MSC (1991):
Primary 33D45; Secondary 42C15
Published electronically:
April 23, 1999
MathSciNet review:
1621949
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: We establish expansion formulas of exponential functions in terms of continuous ultraspherical polynomials, continuous Hermite polynomials and AskeyWilson 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 336205700
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/S0002993999050170
PII:
S 00029939(99)050170
Keywords:
AskeyWilson 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 DMS9625459, the second author was partially supported by NSERC grant A6197, and the third author was partially supported by NSF grant DMS9400510.
Communicated by:
Hal. L. Smith
Article copyright:
© Copyright 1999
American Mathematical Society
