English

A $q$-extension of a partial differential equation and the Hahn polynomials

Combinatorics 2018-05-21 v1 Analysis of PDEs Complex Variables Number Theory

Abstract

Using the theory of analytic functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of qq-partial differential equations, then, it can be expanded in terms of the product of the homogeneous Hahn polynomials. Some non-trivial applications of this expansion theorem to qq-series are discussed.

Keywords

Cite

@article{arxiv.1805.07292,
  title  = {A $q$-extension of a partial differential equation and the Hahn polynomials},
  author = {Zhi-Guo Liu},
  journal= {arXiv preprint arXiv:1805.07292},
  year   = {2018}
}

Comments

arXiv admin note: text overlap with arXiv:1805.02132 and arXiv:1709.06784