${H^{(1)}_{\nu}}\left(z\right)=\frac{\Gamma\left(\tfrac{1}{2}-\nu\right)(\tfrac%
{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{1+i\infty}^{(1+)}e^{izt}(t^{2}-1)^{%
\nu-\frac{1}{2}}\,\mathrm{d}t,$