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

Bouzeffour, Fethi

doi:10.1090/S0002-9939-07-08717-5

A $q$-sampling theorem and product formula for continuous $q$-Jacobi functions
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Proc. Amer. Math. Soc. 135 (2007), 2131-2139 Request permission

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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