FEAT: add spence

[ColmTalbot]

This is an implementation I have of scipy.special.spence for complex input. jax.scipy.special implements the function for real inputs.

This has significant over lap with polylog/Li but matches the scipy API more closely (scipy uses a slightly unusual definition). The current implementation Li gives the generic polylogarithm while this should match

spence(z) = Li(2, 1 - z)

There are also some differences for complex inputs and I think this implementation matches scipy better, for example

In [10]: spence(2 - 0.1j)
Out[10]: np.complex128(-0.8234321080805467+0.06929202401162238j)

In [11]: spexial.spence(2 - 0.1j)
Out[11]: Array(-0.8234399+0.06928854j, dtype=complex64)

In [12]: spexial.Li(2, 1 - (2 - 0.1j))
Out[12]: Array(nan+0.j, dtype=complex64)

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Files with missing lines	Coverage Δ
src/spexial/__init__.py	100.00% <100.00%> (ø)
src/spexial/_src/spence.py	100.00% <100.00%> (ø)

[cgiovanetti]

Looks great, sounds like we could also kill polylog/Li if we implement this? I'd prefer that since scipy.special doesn't have polylog.

[ColmTalbot]

@cgiovanetti personally, I think it's okay to have things that don't have a direct scipy equivalent, and it is documented as such. Do you use polylog with n != 2? If yes, I think we should keep it, if not I could happily go either way.

[ColmTalbot]

I'll add some tests into https://github.com/JAXtronomy/spexial/tree/main/tests/regression matching what is done for gegenbauer.

[cgiovanetti]

@cgiovanetti personally, I think it's okay to have things that don't have a direct scipy equivalent, and it is documented as such. Do you use polylog with n != 2? If yes, I think we should keep it, if not I could happily go either way.

Yeah, we do allow all n < 60 I think. So if you think that it's still useful then I'm happy to leave it, though maybe we should flag somehow that it's not set up for complex inputs.