New series expansions of the F23 function

We can use the power series definition of F23(a1,a2,a3;b1,b2;z) to compute this function for z   in the unit disk only. In this paper we obtain new expansions of this function that are convergent in larger domains. Some of these expansions involve the polynomial F23(a1,−n,a3;b1,b2;z) evaluated at certain points z  . Other expansions involve the Gauss hypergeometric function F12. The domain of convergence is sometimes a disk, other times a half-plane, other times the region |z|2<4|1−z||z|2<4|1−z|. The accuracy of the approximation given by these expansions is illustrated with numerical experiments.