On the -partial differential equations and -series
arXiv:1805.02132
Abstract
Using the theory of functions of several complex variables, we prove that if an analytic function in several variables satisfies a system of -partial differential equations, then, it can be expanded in terms of the product of the Rogers-Szegő polynomials. This expansion theorem allows us to develop a general method for proving -identities. A general -transformation formula is derived, which implies Watson's -analog of Whipple's theorem as a special case. A multilinear generating function for the Rogers-Szegő polynomials is given. The theory of -exponential operator is revisited.
38 pages