Fixing error in integrated term

[dfm]

@ericagol: there was a missing cosh in the derivation of the integrated term for tau < Delta in the manuscript (it was right in the code!), but I found it when deriving the correction for the diagonal of the celerite matrix (which hadn't been implemented correctly before).

[ericagol]

I worked through the algebra, and there was definitely a mistake in my computations (probably in a Mathematica notebook which I can't access right now since my license just expired). I now agree with your equations (C37) and (C38), and it's reassuring that these make more sense based on the symmetry of the equations. Sorry about the error, and I hope it didn't waste too much of your time. Have you tried out the new diagonal term? At some point I would like to take the Fourier transform of the complex kernel to check that it agrees (although it must!).

One thing that might be good would be to change the C1 and C2 in the lines below to match the definition in the paper:

https://github.com/dfm/exoplanet/blob/a86327a0690a0ccd41b5972ab76537acceb1e5bd/exoplanet/gp/terms.py#L363-L364

Nice work!

-Eric

[dfm]

Thanks! It was no problem - just wanted to make sure that I hadn't missed something.

I've updated those lines so that they are consistent with the document now. Thanks!

[ericagol]

Great, thanks!