Generalized binomial coefficient

[PaulXiCao]

This is a pr wrt to issue #282 .
Binomial coefficient is generalized for real/complex arguments using the beta function.

[PaulXiCao]

The make.jl documentation script throws tons of errors. Some are regarding the newly implemented function binomial.

Excerpts from the warnings:

$ cd docs && julia make.jl
...
 Warning: no docs found for 'SpecialFunctions.binomial' in `@docs` block in src/functions_list.md:7-73
...
┌ Warning: no doc found for reference '[`binomial`](@ref)' in src/functions_list.md.
└ @ Documenter.CrossReferences ~/.julia/packages/Documenter/FuXcO/src/CrossReferences.jl:160
...
┌ Warning: no doc found for reference '[`SpecialFunctions.binomial`](@ref)' in src/functions_overview.md.
└ @ Documenter.CrossReferences ~/.julia/packages/Documenter/FuXcO/src/CrossReferences.jl:160
...
┌ Warning: invalid local link: unresolved path in functions_list.md
│   link.text =
│    1-element Array{Any,1}:
│     Markdown.Code("", "binomial")
│   link.url = "@ref"
└ @ Documenter.Writers.HTMLWriter ~/.julia/packages/Documenter/FuXcO/src/Writers/HTMLWriter.jl:1823
...
┌ Warning: invalid local link: unresolved path in functions_overview.md
│   link.text =
│    1-element Array{Any,1}:
│     Markdown.Code("", "binomial(x,y)")
│   link.url = "@ref SpecialFunctions.binomial"
└ @ Documenter.Writers.HTMLWriter ~/.julia/packages/Documenter/FuXcO/src/Writers/HTMLWriter.jl:1823

Any idea what I did wrong?

[codecov]

Codecov Report

Merging #293 (7cc46b5) into master (d18ff04) will increase coverage by 0.04%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #293      +/-   ##
==========================================
+ Coverage   88.17%   88.22%   +0.04%     
==========================================
  Files          11       11              
  Lines        2630     2632       +2     
==========================================
+ Hits         2319     2322       +3     
+ Misses        311      310       -1     

Flag	Coverage Δ
unittests	88.22% <100.00%> (+0.04%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Impacted Files	Coverage Δ
src/gamma.jl	93.86% <100.00%> (+0.28%)	⬆️

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[PaulXiCao]

A Todo list (taken from the issue #282)

• implement the function
• write documentation
  • wikipedia
  • dlmf
• write tests

I didn't find a good link to dlmf. If anybody finds an appropriate link I can include it. I guess it is not that important?

The Documenter.jl script doesn't pick up the function documentation. I already created a topic at discourse.julialang.org.
As there are multiple functions for which the documentations are not picked up I guess it could be handled in a separate issue?

[stevengj]

Type piracy; we would need to use a different name like genbinomial