\[\operatorname{el3}\left(x,k_{c},p\right)=\int_{0}^{\operatorname{arctan}x}%
\frac{\,\mathrm{d}\theta}{({\cos}^{2}\theta+p{\sin}^{2}\theta)\sqrt{{\cos}^{2}%
\theta+k_{c}^{2}{\sin}^{2}\theta}}=\Pi\left(\operatorname{arctan}x,1-p,k\right),\]