doc: add example and doctest for gamma (#462)

docs/make.jl

@@ -1,5 +1,7 @@
 using SpecialFunctions, Documenter
 
+# `using SpecialFunctions` for all doctests
+DocMeta.setdocmeta!(SpecialFunctions, :DocTestSetup, :(using SpecialFunctions); recursive=true)
 makedocs(modules=[SpecialFunctions],
          sitename="SpecialFunctions.jl",
          authors="Jeff Bezanson, Stefan Karpinski, Viral B. Shah, et al.",

src/gamma.jl

@@ -559,6 +559,40 @@ Compute the gamma function for complex ``z``, defined by
 ```
 and by analytic continuation in the whole complex plane.
 
+# Examples
+Special Values:
+```jldoctest
+julia> gamma(0)
+Inf
+
+julia> gamma(1)
+1.0
+
+julia> gamma(2)
+1.0
+```
+
+``\Gamma(0.5)^2 = \pi``
+```jldoctest
+julia> gamma(0.5)^2
+3.1415926535897936
+
+julia> gamma(0.5)^2 ≈ π
+true
+```
+
+For integer `n`: ``\Gamma(n+1) = prod(1:n) = factorial(n)``
+```jldoctest
+julia> gamma(4+1)
+24.0
+
+julia> prod(1:4)  # == 1*2*3*4
+24
+
+julia> gamma(4+1) == prod(1:4) == factorial(4)
+true
+```
+
 External links:
 [DLMF](https://dlmf.nist.gov/5.2.1),
 [Wikipedia](https://en.wikipedia.org/wiki/Gamma_function).