Exponential integral function (#236)

* Add some things

* Test against sympy

* Add more tests

* Use alternate continued fraction

* precision agnotistic checks

* more tests

* some progress

* large real nu seems to work

* remove polynomials dep

* function aliases

* don't need type parameter here

* function names, complex tests

* small fix

* minimax approximation

* handle ArgumentError in tests

* Add to docs

* handle osx test

* test large positive integer nu

* oops

Author: augustt198

Project.toml

@@ -6,8 +6,8 @@ version = "0.10.3"
 OpenSpecFun_jll = "efe28fd5-8261-553b-a9e1-b2916fc3738e"
 
 [compat]
-julia = "1.3"
 OpenSpecFun_jll = "0.5.3"
+julia = "1.3"
 
 [extras]
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"

docs/src/functions_list.md

@@ -63,4 +63,5 @@ SpecialFunctions.beta
 SpecialFunctions.logbeta
 SpecialFunctions.logabsbeta
 SpecialFunctions.logabsbinomial
+SpecialFunctions.expint
 ```

docs/src/functions_overview.md

@@ -23,9 +23,10 @@ Here the *Special Functions* are listed according to the structure of [NIST Digi
 | [`logabsbinomial(x,y)`](@ref SpecialFunctions.logabsbinomial)                                          | accurate `log(abs(binomial(n,k)))` for large `n` and `k` near `n/2`     |
 
 
-## [Trigonometric Integrals](https://dlmf.nist.gov/6)
+## [Exponential and Trigonometric Integrals](https://dlmf.nist.gov/6)
 | Function | Description |
 |:-------- |:----------- |
+| [`expint(nu, z)`](@ref SpecialFunctions.expint) | [exponential integral](https://en.wikipedia.org/wiki/Exponential_integral) ``E_\nu(z)`` |
 | [`sinint(x)`](@ref SpecialFunctions.sinint) | [sine integral](https://en.wikipedia.org/wiki/Trigonometric_integral#Sine_integral) ``Si(x)`` |
 | [`cosint(x)`](@ref SpecialFunctions.cosint) | [cosine integral](https://en.wikipedia.org/wiki/Trigonometric_integral#Cosine_integral) ``Ci(x)`` |
 

src/SpecialFunctions.jl

@@ -57,11 +57,13 @@ export
     zeta,
     sinint,
     cosint,
-    lbinomial
+    lbinomial,
+    expint
 
 include("bessel.jl")
 include("erf.jl")
 include("ellip.jl")
+include("expint.jl")
 include("sincosint.jl")
 include("gamma.jl")
 include("gamma_inc.jl")