I came across this formula in a physics paper(equation 2.28). For $k \gg \omega$, it was stated that the following is true:
${}_2 F_1\hspace{-4pt}\left[\frac{\Delta+i (k+\omega)}{2}, \frac{\Delta-i (k-\omega)}{2} ; \Delta ; x^2\right] \sim e^{[k \sin^{-1} x]}$ where $_2 F_1$ is the ordinary or Gausssian hypergeometric function.
Here $\Delta$ is a positive real number and $k,x$ are real as well. $i$ is the imaginary square root of -1. I don't see how this follows. Any help in arriving at this formula would be appreciated.