English

On a system of $q$-partial differential equations with applications to $q$-series

Complex Variables 2017-09-21 v1

Abstract

Using the theory of functions of several variables and qq-calculus, we prove an expansion theorem for the analytic function in several variables which satisfies a system of qq-partial differential equations. Some curious applications of this expansion theorem to qq-series are discussed. In particular, an extension of Andrews' transformation formula for the qq-Lauricella function is given.

Keywords

Cite

@article{arxiv.1709.06784,
  title  = {On a system of $q$-partial differential equations with applications to $q$-series},
  author = {Zhi-Guo Liu},
  journal= {arXiv preprint arXiv:1709.06784},
  year   = {2017}
}

Comments

15 pages, accepted for the proceedings of the Alladi 60th birthday conference