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Inverse Hankel Function

Provides a function which finds z in the equation hankelh1(ν,z) = h for a given h.

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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.

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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_0 using 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.

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The inverse of the Hankel function

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