Zhiguo Liu, East China Normal U., Shanghai

A q-partial differential equation, complex analysis in several variables and q-series



The concept of q-partial differential equations is first introduced and then we discuss a specific q-partial differential equation. Using the theory of analytic functions in several variables, we prove that any analytic solution of this q-partial differential equation can be expressed in terms of the Rogers-Szego polynomials. This fact allows us to develop a general method of deriving q-hypergeometric identities. Using this method, we can not only give new derivations of many classic q-series identities, but also find new q-formulas.