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A $ q$-sampling theorem and product formula for continuous $ q$-Jacobi functions

Author: Fethi Bouzeffour
Journal: Proc. Amer. Math. Soc. 135 (2007), 2131-2139
MSC (2000): Primary 33D05, 33D15, 33D90, 33C10
Published electronically: February 6, 2007
MathSciNet review: 2299491
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Abstract: In this paper we derive a q-analogue of the sampling theorem for Jacobi functions. We also establish a product formula for the nonterminating version of the q-Jacobi polynomials. The proof uses recent results in the theory of q-orthogonal polynomials and basic hypergeometric functions.

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Additional Information

Fethi Bouzeffour
Affiliation: Institut Préparatoire aux Études d’Ingénieur de Bizerte, Tunisia

Keywords: q-sampling theorem, q-difference, q-special functions
Received by editor(s): February 8, 2006
Received by editor(s) in revised form: March 17, 2006
Published electronically: February 6, 2007
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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