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