\[(-1)^{s+1}d_{s+1}=\frac{a_{s}}{s!}\sum_{k=1}^{s}\frac{1}{k}+\frac{1}{s!}\lim_{%
z\to s+1}\left(\mathscr{M}\mskip-3.0muf\mskip 3.0mu\left(z\right)+\frac{a_{s}}%
{z-s-1}\right),\]