\[S^{m(j)}_{n}\left(z,\gamma\right)=\begin{cases}\psi_{n}^{(j)}(\gamma z)+O\left%
(z^{-2}e^{|\Im z|}\right),&j=1,2,\\
\psi_{n}^{(j)}(\gamma z)\left(1+O\left(z^{-1}\right)\right),&j=3,4.\end{cases}\]