Add ChainRules definitions for gamma(a, x), loggamma(a, x), and gamma_inc

[devmotion]

I added ChainRules definitions for gamma(a, x), loggamma(a, x), and gamma_inc according to https://functions.wolfram.com/GammaBetaErf/GammaRegularized/introductions/Gammas/ShowAll.html. Similar to the Bessel functions, derivatives with respect to the first argument a are not implemented since they are given in terms of a (regularized) hypergeometric function.

Unfortunately, it seems due to the error thrown for derivatives of the first argument these rules can't be tested with test_frule and test_rrule since these functions always unthunk all derivatives. It would be good if one could somehow exclude some derivatives from the tests completely and not only from the finite differencing checks. I'll open an issue in ChainRulesTestUtils regarding this question.

(BTW I assume that due to this issue the derivatives of the Bessel functions are not tested currently)

[codecov]

Codecov Report

Merging #305 (bdd6243) into master (a48ba24) will decrease coverage by 0.96%.
The diff coverage is n/a.

❗ Current head bdd6243 differs from pull request most recent head 98bc7d0. Consider uploading reports for the commit 98bc7d0 to get more accurate results

@@            Coverage Diff             @@
##           master     #305      +/-   ##
==========================================
- Coverage   89.31%   88.35%   -0.97%     
==========================================
  Files          12       12              
  Lines        2640     2653      +13     
==========================================
- Hits         2358     2344      -14     
- Misses        282      309      +27     

Flag	Coverage Δ
unittests	88.35% <ø> (-0.97%)	⬇️

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Impacted Files	Coverage Δ
src/chainrules.jl	100.00% <ø> (ø)
src/gamma_inc.jl	88.20% <0.00%> (-4.24%)	⬇️
src/expint.jl	95.63% <0.00%> (ø)
src/SpecialFunctions.jl	100.00% <0.00%> (ø)

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[stevengj]

Great, thanks! It would be good to resolve the testing question.

[devmotion]

Soon it will be possible to test (existing and new) partially implemented differentials properly: JuliaDiff/ChainRulesTestUtils.jl#140

[andreasnoack]

Should this one be update now that JuliaDiff/ChainRulesTestUtils.jl#140 is merged?

[andreasnoack]

The drone runs seems to have connectivity issues. Not sure why.