\[\zeta\left(z|\mathbb{L}_{\mspace{1.0mu}1}\right)-\zeta\left(z+2K|\mathbb{L}_{%
\mspace{1.0mu}1}\right)+\zeta\left(2K|\mathbb{L}_{\mspace{1.0mu}1}\right)=%
\operatorname{ns}\left(z,k\right),\]