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Incomplete beta function

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Calculates the incomplete beta function Bx(a,b) and the regularized incomplete beta function Ix(a,b).
a
a＞0
b
b＞0
x
0≦x≦1
\(\normalsize Incomplete\ beta\ function\ B_x(a,b)\\ \hspace{70px}and\ regularized\ I_x(a,b)\\ (1)\ B_x(a,b)={\large\int_{\tiny 0}^ {\small x}}t^{a-1}(1-t)^{b-1}dt\\ \hspace{90px} Re(a),Re(b)\gt 0,\hspace{10px} 0\le x\le1\\ (2)\ I_x(a,b)={\large\frac{B_x(a,b)}{B(a,b)}}\\ (2)\ I_x(a,b)+I_{1-x}(b,a)=1\\\)

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