\[\Residue_{z=1}\left[-\zeta^{z-1}\Gamma\left(1-z\right)\mathscr{M}\mskip-3.0muh%
_{2}\mskip 3.0mu\left(z\right)\right]=\left(-\ln\zeta-\gamma\right)-\mathscr{M%
}\mskip-3.0muh_{1}\mskip 3.0mu\left(1\right),\]