\[\widehat{S}_{m}\sim\left(\frac{\pi h}{2(m!)^{2}}\right)^{\ifrac{1}{4}}\left(1-%
\frac{2m+1}{8h}+\dfrac{m^{4}+2m^{3}-121m^{2}-122m-84}{2048h^{2}}+\cdots\right)%
^{-\ifrac{1}{2}}.\]