In this paper we define the q-Laguerre type polynomials Un(x; y; z; q), which
include q-Laguerre polynomials, generalized Stieltjes-Wigert polynomials,
little q-Laguerre polynomials and q-Hermite polynomials as special cases. We
also establish a generalized q-differential operator, with which we build the
relations between analytic functions and Un(x; y; z; q) by using certain
q-partial differential equations. Therefore, the corresponding conclusions
about q-Laguerre polynomials, little q-Laguerre polynomials and q-Hermite
polynomials are gained as corollaries. As applications, some generating
functions and generalized Andrews-Askey integral formulas are given in the
final section.
On a system of partial differential equations and the bivariate Hermite polynomials
