\[\int_{0}^{z}\mathbf{M}_{0}\left(t\right)\,\mathrm{d}t+\frac{2}{\pi}(\ln\left(2%
z\right)+\gamma)\sim\frac{2}{\pi}\sum_{k=1}^{\infty}\frac{(2k)!(2k-1)!}{(k!)^{%
2}(2z)^{2k}},\]