\[F_{\ell}\left(\eta,\rho\right)=C_{\ell}\left(\eta\right)2^{-\ell-1}(\mp\mathrm%
{i})^{\ell+1}M_{\pm\mathrm{i}\eta,\ell+\frac{1}{2}}\left(\pm 2\mathrm{i}\rho%
\right),\]