added Logarithmic integral function

[Bumblebee00]

I added the Logarithmic integral function definied as

$$li(x) = \int_{0}^x \frac{1}{\ln{t}} \mathrm{dt},$$

As is written here I implemented it as Ei(ln(x)) where Ei is the expinti function.

I also updated the docs, I hope to have done everything correctly but it's my first time contributing here so I am not sure.

I want to add this function becasue I am writing a symbolic integration software and I need to implement the result of the integral 1/ln(x)

[codecov]

Codecov Report

❌ Patch coverage is 83.33333% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 94.09%. Comparing base (31e3c1a) to head (c3406d3).
⚠️ Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
src/expint.jl	83.33%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #500      +/-   ##
==========================================
+ Coverage   94.07%   94.09%   +0.01%     
==========================================
  Files          14       14              
  Lines        2905     2911       +6     
==========================================
+ Hits         2733     2739       +6     
  Misses        172      172              

Flag	Coverage Δ
unittests	94.09% <83.33%> (+0.01%)	⬆️

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[devmotion]

This creates a type instability.

[Bumblebee00]

could this solve it?

    elseif x == 0
        return zero(typeof(x))

[oscardssmith]

or simply zero(x)

[oscardssmith]

but you probably want zero(float(x))

[devmotion]

Suggested change

	@test li(0.0) == 0
	@test li(1.0) == -Inf
	@test li(Inf) === Inf
	@test li(2) ≈ 1.0451637801174927
	@test @inferred(li(0.0)) === 0.0
	@test @inferred(li(1.0)) === -Inf
	@test @inferred(li(Inf)) === Inf
	@test @inferred(li(2)) ≈ 1.0451637801174927

[devmotion]

Maybe add tests with Float32 as well, also to ensure that there are no unintended promotions to Float64?

[Bumblebee00]

I just don't understand why:

julia> @inferred(li(2)) 
ERROR: return type Float64 does not match inferred return type Union{Float64, Int64}

in this case is wanted that calling the function with a int returns a float, right?

[oscardssmith]

that is correct.

[devmotion]

Maybe a more descriptive name such as logintegral (see https://reference.wolfram.com/language/ref/LogIntegral.html) would be better?

[oscardssmith]

li is the common name in math, we could go logint to match expinti..