Incomplete Beta function $\text{B}_x(\alpha,\beta)$ approximation for large $\alpha,\beta$?

Question

I need good asymptotic approximations to the incomplete Beta function $\text{B}_x(\alpha,\beta)$ for large values of $\alpha,\beta$. Specifically, I need approximations valid for the following regimes:

• $\alpha > 100, \beta < 100$
• $\alpha < 100, \beta > 100$
• $\alpha,\beta > 100$