Hypergeometric connection formula at infinity
= Hypergeometric connection formula at infinity
Away from resonant parameter cases, two independent local solutions at infinity are
$$
z^{-a}F(a,1+a-c;1+a-b;z^{-1})
$$
and the expression obtained by exchanging $a$ and $b$. Every analytic continuation of a hypergeometric solution into their common domain is a constant linear combination of this basis.