Add docs for new hypergeometric functions

[andrjohns]

Submission Checklist

• [x] Builds locally
• [x] New functions marked with <<{ since VERSION }>>
• [x] Declare copyright holder and open-source license: see below

Summary

Corresponding docs PR for the newly-exposed hypergeometric functions

I've made a separate section for these, since there will be more specialisations coming - but let me know if they should be somewhere else!

Copyright and Licensing

Please list the copyright holder for the work you are submitting (this will be you or your assignee, such as a university or company): Andrew Johnson

By submitting this pull request, the copyright holder is agreeing to license the submitted work under the following licenses:

• Code: BSD 3-clause (https://opensource.org/licenses/BSD-3-Clause)
• Documentation: CC BY-ND 4.0 (https://creativecommons.org/licenses/by-nd/4.0/)

[WardBrian]

This should mention the size constraints on p,q (I think it's just that length(p) == length(q) - 1?)

We could also put some of the math in the "mathematical functions" appendix -- not really sure we use that all that much though

[WardBrian]

Going to ask @bob-carpenter if he can take a look at this

[spinkney]

Are these functions in the new release?

[WardBrian]

@spinkney yes! so it would be nice to get this reviewed and merged in the next week

[spinkney]

Other than the first equation, this looks great. Intense, and I have no idea what it's useful for, but the doc looks good.

Just wanted to chime in and say this is useful in constructing cdfs for some discrete distributions. These can then be used in copulas with data augmentation for the discrete margins. I'm sure that there are plenty of other use cases as well!

[bob-carpenter]

Thanks, @spinkney. We're working on getting a copulas chapter into the User's Guide at which point it might be nice to add the how-to. Speaking of which, there are probably other of the tricks you have in your library that'd be useful to document in the User's Guide.

[spinkney]

@andrjohns has a really nice copula post at https://users.aalto.fi/~johnsoa2/notebooks/CopulaIntro.html. He also has one about linking base R functions written in C to Stan https://users.aalto.fi/~johnsoa2/notebooks/R_C_Math.html.

We should get a discussion on discourse about things to add to the SUG. I'm all for copulas being added. I think a section on modeling with the newly exposed constraint transform functions is worthwhile. I'm using those things all the time!