\[{\mathscr{Z}_{\nu}}^{(k)}\left(z\right)=\frac{1}{2^{k}}\left(\mathscr{Z}_{\nu-%
k}\left(z\right)+\genfrac{(}{)}{0.0pt}{}{k}{1}\mathscr{Z}_{\nu-k+2}\left(z%
\right)+\genfrac{(}{)}{0.0pt}{}{k}{2}\mathscr{Z}_{\nu-k+4}\left(z\right)+%
\cdots+\mathscr{Z}_{\nu+k}\left(z\right)\right).\]