\[\frac{1}{M\left(a_{0},g_{0}\right)}=\frac{2}{\pi}\int_{0}^{\pi/2}\frac{\,%
\mathrm{d}\theta}{\sqrt{a_{0}^{2}{\cos}^{2}\theta+g_{0}^{2}{\sin}^{2}\theta}}=%
\frac{1}{\pi}\int_{0}^{\infty}\frac{\,\mathrm{d}t}{\sqrt{t(t+a_{0}^{2})(t+g_{0%
}^{2})}}.\]