I need asymptotic approximations of the Hypergeometric function $_2F_1(a,b;c;x)$ for large positive values of $a, b, c$. Specifically, I need approximations for all the possible regimes, in which one or more of $a,b,c$ are greater than 100, and the others are positive and less than 100.
$x$ is in the range $0<x<1$.