\[{H^{-}_{\ell}}\left(\eta,\rho\right)=\frac{-\mathrm{i}e^{-\pi\eta}\rho^{\ell+1%
}}{(2\ell+1)!C_{\ell}\left(\eta\right)}\int_{0}^{\infty}\left(\frac{\exp\left(%
-\mathrm{i}(\rho\tanh t-2\eta t)\right)}{(\cosh t)^{2\ell+2}}+\mathrm{i}(1+t^{%
2})^{\ell}\exp\left(-\rho t+2\eta\operatorname{arctan}t\right)\right)\,\mathrm%
{d}t,\]