${\displaystyle x\in [0,1)}$

${\displaystyle f(x)={\frac {1}{\pi {\sqrt {x(1-x)))))}$

${\displaystyle F(x)={\frac {2}{\pi ))\arcsin \left({\sqrt {x))\right)}$

${\displaystyle {\frac {1}{2))}$

${\displaystyle {\frac {1}{2))}$

${\displaystyle x\in \{0,1\))$

${\displaystyle {\tfrac {1}{8))}$

0

${\displaystyle -{\tfrac {3}{2))}$

${\displaystyle \ln {\tfrac {\pi }{4))}$

${\displaystyle 1+\sum _{k=1}^{\infty }\left(\prod _{r=0}^{k-1}{\frac {2r+1}{2r+2))\right){\frac {t^{k)){k!))}$

${\displaystyle {}_{1}F_{1}({\tfrac {1}{2));1;i\,t)}$