I am trying to find out which are the generating functions related to Gauss hypergeometric function. I mean not only the most general:
$$G(x,y,z,t) = \sum_{a,b,c=0}^\infty {_2F_1(a,b;c;t)x^{a}y^{b}z^{c}}$$
but also any restriction summing up only some of the a, b and c parameters.
Any suggestion would be valuable.
Thanks