Generalised Zernike polynomials?

[Sheehan Olver]

I remember there used to be docs on what the transforms actually do, but they seem to have disappeared from the docs page! Where's the Disk transform definition, for example??

[Mikael Slevinsky]

The doxygen layout is kinda strange in that any added pages are under the "Related Page" tab, so is this what you were remembering? https://mikaelslevinsky.github.io/FastTransforms/transforms.html

[Sheehan Olver]

Thanks!! @TSGut here's the link

We actually want to do generalised Zernike polynomials. That is, orthogonal w.r.t. (1-r^2)^β. Is that possible?

[Mikael Slevinsky]

These are spin-weighted Zernike? or different?

[Sheehan Olver]

Don't think so...

[Sheehan Olver]

They are just like Zernike but with β in the Jacobi paramters somewhere

[Mikael Slevinsky]

It should be possible to support orthonormality with respect to r^a (1-r^2)^b on the disk.

[Mikael Slevinsky]

A pull request will soon appear for generalized Zernike polynomials, orthonormal w.r.t L^2(D^2, r^{2α+1}(1-r^2)^β dr dθ).