Hankel functions

Summary

The Hankel functions $H^{(1)}_\nu$ and $H^{(2)}_\nu$ are the Bessel functions of the third kind. They are the complex combinations $J_\nu \pm i Y_\nu$ of the Bessel functions of the first kind and of the second kind. They play the role of $e^{\pm i x}$ next to the roles of $\cos x$ and $\sin x$ played by $J_\nu$ and $Y_\nu$. They describe outgoing and incoming cylindrical waves.