\[E\left(k\right)=\frac{\pi}{2}\sum_{m=0}^{\infty}\frac{{\left(-\tfrac{1}{2}%
\right)_{m}}{\left(\tfrac{1}{2}\right)_{m}}}{m!\;m!}k^{2m}=\frac{\pi}{2}{{}_{2%
}F_{1}}\left({-\tfrac{1}{2},\tfrac{1}{2}\atop 1};k^{2}\right),\]