\[(-1)^{m}W_{\kappa,\mu}\left(ze^{2m\pi\mathrm{i}}\right)=-\frac{e^{2\kappa\pi%
\mathrm{i}}\sin\left(2m\mu\pi\right)+\sin\left((2m-2)\mu\pi\right)}{\sin\left(%
2\mu\pi\right)}W_{\kappa,\mu}\left(z\right)-\frac{\sin\left(2m\mu\pi\right)2%
\pi\mathrm{i}e^{\kappa\pi\mathrm{i}}}{\sin\left(2\mu\pi\right)\Gamma\left(%
\frac{1}{2}+\mu-\kappa\right)\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}W_{-%
\kappa,\mu}\left(ze^{\pi\mathrm{i}}\right).\]