\[{\psi}^{(n)}\left(z\right)\sim(-1)^{n-1}\left(\frac{(n-1)!}{z^{n}}+\frac{n!}{2%
z^{n+1}}+\sum_{k=1}^{\infty}\frac{(2k+n-1)!}{(2k)!}\frac{B_{2k}}{z^{2k+n}}%
\right).\]