\[\int^{\infty}_{0}f(x)g(yx)\,\mathrm{d}x=\frac{1}{2\pi\mathrm{i}}\*\int^{\sigma%
+\mathrm{i}\infty}_{\sigma-\mathrm{i}\infty}y^{-s}\mathscr{M}\mskip-3.0muf%
\mskip 3.0mu\left(1-s\right)\mathscr{M}\mskip-3.0mug\mskip 3.0mu\left(s\right)%
\,\mathrm{d}s,\]