$h\left(ϵ,\ell ;r\right)={\left(\frac{2}{\pi \tau }\frac{A\left(ϵ,\ell \right)}{1-e^{-2\pi /\tau }}\right)}^{\frac{1}{2}}{G}_{\ell }\left(-1/\tau ,\tau r\right)$