\[\frac{{\mathrm{d}}^{m}}{{\mathrm{d}s}^{m}}\mathcal{S}\mskip-3.0muf\mskip 3.0mu%
\left(s\right)=(-1)^{m}m!\int^{\infty}_{0}\frac{f(t)\,\mathrm{d}t}{(s+t)^{m+1}},\]