Yet another basic analogue of Grafʹs addition formula

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