Yet another basic analogue of Graf's addition formula
Classical Analysis and ODEs
2016-09-06 v1
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 tends to . The corresponding product formula is derived. Some known identities for Jackson's -Bessel functions are obtained as limiting cases. As special cases we prove identities for -Charlier polynomials.
Cite
@article{arxiv.math/9409231,
title = {Yet another basic analogue of Graf's addition formula},
author = {Erik Koelink},
journal= {arXiv preprint arXiv:math/9409231},
year = {2016}
}