Inverse Hankel Function
Provides a function which finds
z in the equation
hankelh1(ν,z) = h for a
To install this package, call
import Pkg Pkg.add("https://github.com/jondea/InverseHankelFunction.jl")
or alternatively type
] add https://github.com/jondea/InverseHankelFunction.jl
in the REPL.
For a given
h there are typically many solutions to the equation, so to define
a single valued function, we take two approaches:
- Define a "normalised" Hankel function
hbar(z) = h(z)/h(z_0), and analytically continue our inverse from the point
z_0. This is currently the best studied and most completely implemented approach, and we discuss it here. In a related way, we also define the inverse Hankel function which "passes through"
z_0using the interface
invhankelh1(ν, h, PassingThrough(z_0))
- A more general approach is to define a branch index (which we denote as
b) and find a way to enumerate them. This approach is less well developed, and we discuss it here.