Added PN stuff (not tested)

[jakobneef]

This adds support for PN series of TeukolskyRadialPN and TeukolskyPointParticleModePN

[barrywardell]

I'm having trouble getting TeukolskyPointParticleModePN. The output includes things like SpinWeightedSpheroidalHarmonicS[-2, 2, 2, 2 a \[CapitalOmega]Kerr][\[Pi]/2, 0]. Is there an updated to SpinWeightedSpheroidalHarmonics required to get it to work?

[barrywardell]

Also a few more comments:

• There is a new symbol \[CapiatlOmega]Kerr exposed by TeukolskyPointParticleModePN. Is there a better, non-hacky way to achieve this? Perhaps write \[CapiatlOmega]Kerr explicitly in terms of p and a?
• When the amplituudes are not computed, we should probably return them as Missing["NotComputed"]
• The documentation refers to setting options to "True" (with quotes). Should this be True (without quotes)?
• When returning a RadialFunction from a mode, should we just return a TeukolskyRadialFunctionPN? This would avoid the aesthetic problems mentioned in the documentation.
• There are some typos in the documentation, eg. a link with just ::

[jakobneef]

• The issue with the SpinWeightedSpheroidalHarmonicS and the \[CapiatlOmega]Kerr are related. It would be possible to express \[CapiatlOmega]Kerr as 1\(r0^(3\2)+a), however to be consistent we would have to PN expand that expression, since r0 carries powers of eta. To be consistent then as well we would have to expand the SpinWeightedSpheroidalHarmonicS and it's derivatives as they depend on OmegaKerr. At the moment we opted against this to allow the user to get the coefficients of the S, S' and S''. To be honest I am unhappy with both possible options and very open to input on that question.
• I'll fix that.
• I'll fix that.
• I'm not sure I understand that point. Maybe we can discuss it tomorrow?
• I'll fix that

Thanks for the testing! I'll work in the fixes tomorrow.

[barrywardell]

It looks like most things are now resolved. Are there any outstanding issues?

[jakobneef]

Only thing is I haven't updated the documentation to the changes I made today. I doubt it will take me longer than a day.

[barrywardell]

I've updated the documentation, so I think that's everything and the PR is ready to be merged.

[barrywardell]

All comments have been resolved