Computing the Zernike polynomials coefficients?

[Veenty]

I want to expand a function on the unit disk using the Zernike polynomials. I've seen that the domain Disk exists, but I cannot find that much documentation on how to use it, and nothing about Zernike polynomials. However all the pieces are there, so it should be possible.

[dlfivefifty]

You can do this with https://github.com/JuliaApproximation/MultivariateOrthogonalPolynomials.jl

using MultivariateOrthogonalPolynomials, ContinuumArrays
Z = Zernike()
f = (x,y) -> exp(x*cos(y)) # function to be expanded
expand(Z, 𝐱 -> f(𝐱...))

The long term goal is to have ApproxFun.jl sit on top of ContinuumArrays.jl