\[D\left(k\right)=\frac{\pi}{4}\sum_{m=0}^{\infty}\frac{{\left(\tfrac{3}{2}%
\right)_{m}}{\left(\tfrac{1}{2}\right)_{m}}}{(m+1)!\;m!}k^{2m}=\frac{\pi}{4}{{%
}_{2}F_{1}}\left({\tfrac{3}{2},\tfrac{1}{2}\atop 2};k^{2}\right),\]