\[\int e^{iz}z^{\nu}\mathscr{C}_{\nu}\left(z\right)\,\mathrm{d}z=\frac{e^{iz}z^{%
\nu+1}}{2\nu+1}(\mathscr{C}_{\nu}\left(z\right)-i\mathscr{C}_{\nu+1}\left(z%
\right)),\]