$$x=F^{-1.}\left(P|{\nu }_{1.},{\nu }_{2.}\right)=\left\{x:F\left(x|{\nu }_{1.},{\nu }_{2.}\right)=P\right\}$$

$$P=F(x|{\nu }_{1.},{\nu }_{2.})={\displaystyle \underset{0}{\overset{x}{\int }}\frac{\Gamma \left[\frac{({\nu }_{1.}+{\nu }_{2.})}{2.}\right]}{\Gamma \left(\frac{{\nu }_{1.}}{2.}\right)\Gamma \left(\frac{{\nu }_{2.}}{2.}\right)}}{\left(\frac{{\nu }_{1.}}{{\nu }_{2.}}\right)}^{\frac{{\nu }_{1.}}{2.}}\frac{T^{\frac{{\nu }_{1.}-2.}{2.}}}{{\left[1.+\left(\frac{{\nu }_{1.}}{{\nu }_{2.}}\right)T\right]}^{\frac{{\nu }_{1.}+{\nu }_{2.}}{2.}}}DT$$