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



What is the value of the regularized incomplete beta function at x=0.5?
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?


