English

A unified approach to $q$-special functions of the Laplace type

Classical Analysis and ODEs 2011-03-29 v1

Abstract

We propose a unified approach to qq-special functions, which are degenerations of basic hypergeometric functions 2ϕ1(a,b;c;q,x){}_2\phi_1(a,b;c;q,x). We obtain a list of seven different class of qq-special functions: 2ϕ1,1ϕ1{}_2\phi_1, {}_1\phi_1, two different types of the qq-Bessel functions, the qq-Hermite-Weber functions, two different types of the qq-Airy functions. We show that there exist a relation between two types of the qq-Airy functions.

Keywords

Cite

@article{arxiv.1103.5232,
  title  = {A unified approach to $q$-special functions of the Laplace type},
  author = {Yousuke Ohyama},
  journal= {arXiv preprint arXiv:1103.5232},
  year   = {2011}
}