\[\operatorname{me}_{\nu}'\left(0,h^{2}\right){\operatorname{M}^{(j)}_{\nu}}%
\left(z,h\right)=\mathrm{i}\tanh z\sum_{n=-\infty}^{\infty}(-1)^{n}(\nu+2n)c_{%
2n}^{\nu}(h^{2}){\cal C}_{\nu+2n}^{(j)}(2h\cosh z),\]