\(\normalsize Incomplete\ beta\ functions\ B_x(a,b),\ I_x(a,b)\\ (1)\ Incomplete\ beta\ function\\ \hspace{40px}B_{x}(a,b)={\large\int_{\small 0}^{\hspace{25px}x}}t^{a-1}(1-t)^{b-1}dt\\ (2)\ Regularized\ incomplete\ beta\ function\\ \hspace{40px}I_{x}(a,b)={\large\frac{B_{x}(a,b)}{B(a,b)}}\\ (3)\ Complete\ beta\ function\\ \hspace{40px}B(a,b)={\large\int_{\small 0}^{\small 1}}t^{a-1}(1-t)^{b-1}dt\\ \) |
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