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Yet another basic analogue of Graf's addition formula

Erik Koelink
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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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Erik Koelink. 1994-09-21. Yet another basic analogue of Graf's addition formula. https://arxiv.org/abs/math/9409231

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