$${\text{f}}_{n,m}\left(x\right)=\frac{m^{\frac{m}{2}}{n}^{\frac{n}{2}}{x}^{\frac{n}{2}-1}}{{\left(m+nx\right)}^{\frac{\left(n+m\right)}{2}}B\left(\frac{n}{\mathrm{2,}}\frac{m}{2}\right)}$$