$$Y=F(x|{\nu }_{1.},{\nu }_{2.})=\frac{\Gamma \left[\frac{({\nu }_{1.}+{\nu }_{2.})}{2.}\right]}{\Gamma \left(\frac{{\nu }_{1.}}{2.}\right)\Gamma \left(\frac{{\nu }_{2.}}{2.}\right)}{\left(\frac{{\nu }_{1.}}{{\nu }_{2.}}\right)}^{\frac{{\nu }_{1.}}{2.}}\frac{x^{\frac{{\nu }_{1.}-2.}{2.}}}{{\left[1.+\left(\frac{{\nu }_{1.}}{{\nu }_{2.}}\right)x\right]}^{\frac{{\nu }_{1.}+{\nu }_{2.}}{2.}}}$$