What is $I_{0.5}(a,b)$ where I is the regularized incomplete beta function?

You mean this? http://en.wikipedia.org/wiki/Beta_function $$ \frac{\int_{0}^{\frac{1}{2}} t^{a  1} (1  t)^{b  1} d t}{\int_{0}^{1} t^{a  1} (1  t)^{b  1} d t} = \\ \quad{}\quad{}\frac{\mathrm{hypergeom} \Bigl([a,b + 1],[1 + a],\frac{1}{2}\Bigr) \Gamma (a + b)}{2^{a} a \Gamma (b) \Gamma (a)} $$ Why do you think there is anything simpler in general? 

