\[\rselection{{H^{(1)}_{\nu}}\left(\nu z\right)\\
{H^{(2)}_{\nu}}\left(\nu z\right)}\sim 2e^{\mp\pi i/3}\left(\frac{4\zeta}{1-z^%
{2}}\right)^{\frac{1}{4}}\left(\frac{\operatorname{Ai}\left(e^{\pm 2\pi i/3}%
\nu^{\frac{2}{3}}\zeta\right)}{\nu^{\frac{1}{3}}}\sum_{k=0}^{\infty}\frac{A_{k%
}(\zeta)}{\nu^{2k}}+\frac{e^{\pm 2\pi i/3}\operatorname{Ai}'\left(e^{\pm 2\pi i%
/3}\nu^{\frac{2}{3}}\zeta\right)}{\nu^{\frac{5}{3}}}\sum_{k=0}^{\infty}\frac{B%
_{k}(\zeta)}{\nu^{2k}}\right),\]