I am working on this paper, regarding the spectrum of a certain operator in the hyperbolic plane, and at a certain point are presented with an hypergeometric function \begin{equation} \text{}_2 F_1\left(t-b, t-b;2t;\frac{1}{1-\sigma}\right) \end{equation} which they explore in a large limit of a variable $a \to \infty$ that, to leading order, leads to the approximations \begin{equation} \frac{1}{1-\sigma} \sim- \frac{r^2}{4a^2} \end{equation} \begin{equation} t \sim Ba^2 + \frac{1}{2} - \frac{2E}{B} \end{equation} and then they state that in this limit the hypergeometric function goes to the Whittaker function(equation 5.10) \begin{equation} \text{}_2F_1\left(t-b, t-b;2t; \frac{1}{1-\sigma} \right) \sim \rho ^{-2E/B} e^{\rho/2} \,W_{2E/B, 0}(\rho) \end{equation} where $b = Ba^2$ and $\rho = Br^2/2$.
I'm having trouble demonstrating that we get this relation between these 2 functions in the limit $a\to \infty$.