removed factorial

[PaulXiCao]

Base.factorial is extended in SpecialFunction.jl.

This is type piracy and doesn't follow Julia's style guide.

There is at least one problem with it for which we did not find a solution so far:
The method Base.factorial(x::BigFloat) assumes x::UInt and therefor, we cannot overwrite it using the gamma function for arbitrary BigFloats. There is also an issue #232 for it.

As stated by stevengj at issue #296 one should much rather just call gamma for non-integer arguments directly. Thus, there is no need for an extended factorial function.

[codecov]

Codecov Report

Merging #297 (6b4dfff) into master (281292f) will increase coverage by 0.02%.
The diff coverage is n/a.

@@            Coverage Diff             @@
##           master     #297      +/-   ##
==========================================
+ Coverage   88.17%   88.20%   +0.02%     
==========================================
  Files          11       11              
  Lines        2630     2628       -2     
==========================================
- Hits         2319     2318       -1     
+ Misses        311      310       -1     

Flag	Coverage Δ
unittests	88.20% <ø> (+0.02%)	⬆️

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

Impacted Files	Coverage Δ
src/gamma.jl	93.79% <ø> (+0.22%)	⬆️

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[simonbyrne]

The gamma function is also not the only function that interpolates the factorials, e.g. https://en.wikipedia.org/wiki/Hadamard%27s_gamma_function

[stevengj]

I'm generally fine with this. However, since it is a breaking change, it would be good to survey packages using SpecialFunctions to get a sense for whether they rely on this…

[PaulXiCao]

factorial(x::BigFloat)

The following search on github.com
"org:JuliaMath factorial(big"
yields only 5 results and all use BigInt.

Another search
"language:Julia factorial(BigFloat"
yields no results at all.

A more general search
"language:Julia factorial(big"
yields more than 250 results but as I scanned the first couple of them I only found usage of BigInts.

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factorial(x::Float)

The search "language:Julia factorial(Float" yields 6 results.
This reposity will actually need to change their code because of this pr.

The search "https://github.com/JulHoltzDevelopers/WavesAndEigenvalues.jl" yields no result.

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Those were just the first searches that popped to my mind. But it seems to me like SpecialFunctions.factorial is not used very widely.

[ViralBShah]

Can we merge this and bump the minor version number to signal the API change?