Notes on q-Partial Differential Equations for q-Laguerre Polynomials and Little q-Jacobi Polynomials.

This article defines two common q-orthogonal polynomials: homogeneous q-Laguerre polynomials and homogeneous little q-Jacobi polynomials. They can be viewed separately as solutions to two q-partial differential equations. Furthermore, an analytic function satisfies a certain system of q partial differential equations if and only if it can be expanded in terms of homogeneous q-Laguerre polynomials or homogeneous little q-Jacobi polynomials. As applications, several generalized Ramanujan q-beta integrals and Andrews-Askey integrals are obtained. [ABSTRACT FROM AUTHOR]