Missing incomplete Beta function and its logarithm

[cossio]

Currently the standard library has no incomplete Beta function, or its logarithm:

log(B(\alpha, \beta, x))

which can be useful in some applications.

[cossio]

related: #16177

[andreasnoack]

For a summary of the history of "The Incomplete Beta Function in Julia" see https://groups.google.com/forum/#!searchin/julia-dev/Incomplete$20beta$20function/julia-dev/4dK0CuVvxrQ/8hLDO5UAsEAJ. To some extend, this is also dup of #4301 although it might be useful to have specific issues for each special function.

[simonbyrne]

You can use StatsFuns.jl, or Distributions.jl.

I think the general consensus of #4301/#8536 is that we probably won't add more special functions to Base.

[cossio]

@simonbyrne Thanks for pointing out StatsFuns.jl, looks awesome, and it seems to include the logarithm of the incomplete Beta functions.

Although maybe a better organization is to have a dedicated module SpecialFuns.jl as a dependancy of both StatsFuns.jl and Distributions.jl, instead of duplicating code.

[kshyatt]

@cossio, is your issue resolved? Can I close this, since you've found a package that suits your needs?