# Inverting the asymptotic expansion of Gauss Hypergeometric Function

I am interested in obtaining the asymptotic expansion of $$r(\rho)$$ (which is the inverse of the object rho[r_,b_,q_] below). Basically I want to series expand rho[r_,b_,q_] for large $$r$$ (i.e. as $$r\to \infty$$) and then invert the series to obtain $$r(\rho)$$. I have tried the $$\textbf{InverseSeries}$$ function in Mathematica but I am not really sure if I am doing the right thing. By the way, $$b$$ is just some positive constant while $$-\infty.

rho[r_,b_,q_]:=(2b/(1-q))(1-(b/r)^(1-q))^(1/2)Hypergeometric2F1[1/2,1-1/(q-1),3/2,1-(b/r)^(1-q)]