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