Zhiguo Liu, East China Normal U., Shanghai A qpartial differential equation,
complex analysis in several variables and qseries
Abstract The concept of qpartial differential equations is first introduced and then we discuss a specific qpartial differential equation. Using the theory of analytic functions in several variables, we prove that any analytic solution of this qpartial differential equation can be expressed in terms of the RogersSzego polynomials. This fact allows us to develop a general method of deriving qhypergeometric identities. Using this method, we can not only give new derivations of many classic qseries identities, but also find new qformulas.
