extend binomial to real and complex numbers

[musm]

Originally from: https://github.com/JuliaLang/julia/pull/14165

[stevengj]

Having a binomial(x,y) = inv((x+1)*beta(x - y + 1, y + 1)) method or similar seems reasonable.

[PaulXiCao]

I'd like to work on this. I have the following things in mind

• implement the function
  • exactly the one-liner that @stevengj wrote before
• write documentation (link to dlmf, wikipedia)
• write tests
  • compare to integer inputs
  • compare some random arguments
  • compare complex arguments
  • compare mixed (real, complex) arguments
  • checking BigFloat implementation?

Anything else to keep in mind?

[stevengj]

That seems like it.