\[\mathscr{C}_{\nu}\left(\lambda z\right)=\lambda^{\pm\nu}\sum_{k=0}^{\infty}%
\frac{(\mp 1)^{k}(\lambda^{2}-1)^{k}(\tfrac{1}{2}z)^{k}}{k!}\mathscr{C}_{\nu%
\pm k}\left(z\right),\]