Test LCMC
Formula 10.4.15:
$\mathrm{Ai}(-z)=\frac{1}{3}\sqrt{z} [J_{1/3}(\zeta)+J_{-1/3}(\zeta)]=\frac{1}{2}\sqrt{z/3}[e^{\pi i/6}H^{(1)}_{1/3}(\zeta)+e^{-\pi i/6}H^{(2)}_{1/3}(\zeta)]$