Spherical Hankel function
= Spherical Hankel function
{title2=$h_n^{(1)}=j_n+iy_n,\quad h_n^{(2)}=j_n-iy_n$}
These combinations of <Spherical Bessel functions> solve the radial <Helmholtz equation>. For time dependence $e^{-i\omega t}$, $h_n^{(1)}(kr)$ is outgoing and $h_n^{(2)}(kr)$ incoming. At fixed order and large argument, $h_n^{(1)}(t)\sim(-i)^{n+1}e^{it}/t$. Their recurrence is $h_{n+1}=(2n+1)h_n/t-h_{n-1}$.