ENH: integrate Arnie Van Buren's implementations of the spheroidal wave functions

[person142]

We currently rely on the implementations of spheroidal wave functions in specfun. @MathieuandSpheroidalWaveFunctions has developed greatly improved implementations, which are now on Github:

https://github.com/MathieuandSpheroidalWaveFunctions

and MIT licensed. Integrate them and see which of these bugs they resolve (I rather suspect all of them):

• Spheroid Wave Functions (special.obl_rad1, .obl_rad2, .pro_rad1, .pro_rad2) not returning values for negative numbers #13968
• Radial spheroidal wavefunctions can all segfault #6211
• Unexpected behavior of pro_rad1 for x < 1.0 #5227
• Incorrect return for oblate spheroidal radial function of the 2nd kind #3777

[person142]

Ping @tupui since we were talking about this over in #13968.

[tupui]

Thanks for the ping. This looks definitely like a good idea as current functions are partially broken.

[ivalaginja]

Hi! Has there been any progress on this?

[tupui]

Hi @ivalaginja. I am afraid not. It's basically waiting for someone to take the time to work on this. Any help is appreciated 😃