English

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 qq tends to 11. The corresponding product formula is derived. Some known identities for Jackson's qq-Bessel functions are obtained as limiting cases. As special cases we prove identities for qq-Charlier polynomials.

Keywords

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}
}