On the q-Partial Differential Equations and q-Series

By Zhi-Guo Liu. 2018

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Using the theory of functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of q-partial differential equations, then, it can be expanded in terms of the product of the Rogers-Szegý o poly- nomials. This expansion theorem allows us to develop a general method for proving q-identities. A general q-transformation formula is derived, which implies Watson's q-analog of Whipple's theorem as a special case. A multilinear generating function for the Rogers-Szegý o polynomials is given. The theory of q-exponential operator is revisited.

Subfields: Algebra and Number Theory, Applied Mathematics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bbe5d50a81cead87d3fcbb33bfb1dbe2d8f5e867