Yet another basic analogue of Graf's addition formula
Abstract
An identity involving basic Bessel functions and Al-Salam--Chihara polynomials is proved for which we recover Graf's addition formula for the Bessel function as the base q tends to 1. The corresponding product formula is derived. Some known identities for Jackson's q-Bessel functions are obtained as limiting cases. As special cases we prove identities for q-Charlier polynomials.
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