Quadratic $q$-exponentials and connection coefficient problems
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- by Mourad E. H. Ismail, Mizan Rahman and Dennis Stanton PDF
- Proc. Amer. Math. Soc. 127 (1999), 2931-2941 Request permission
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.References
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Additional Information
- Mourad E. H. Ismail
- Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
- MR Author ID: 91855
- 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
- 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
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1621949