Incomplete beta function
From specialfunctionswiki
The incomplete beta function is defined by $$B_x(a,b)=\displaystyle\int_0^x t^{a-1}(1-t)^{b-1} dt.$$
Properties
Theorem
The following formula holds: $$B_x(a,b)=\dfrac{x^a}{a} {}_2F_1(a,1-b;a+1;x),$$ where $B_x$ denotes the incomplete beta function and ${}_2F_1$ denotes the hypergeometric pFq.
