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