Meijer $G$ function and Lauricella Functions

Question

As everyone know Meijer $G$ function is a vary general function that includes most of the known special functions; is it possible to consider Lauricella Functions as a special case of $G$?

Answer 1

No. Meijer $G$-function is equivalent to generalized hypergeometric function $_pF_q(\ldots;z)$ in one variable. Lauricella functions are generalizations of $_2F_1(\ldots;z)$ to many variables $z_1,\ldots,z_n$.

As you see, the directions of generalizations are different and concern the number of parameters in the former case and the number of arguments in the latter. The "intersection" of the two constructions is given by the Gauss hypergeometric series $_2F_1$.