add a positive₂F₁ for the incomplete beta function in stats

Author: MikaelSlevinsky

Project.toml

@@ -1,6 +1,6 @@
 name = "HypergeometricFunctions"
 uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
-version = "0.3.8"
+version = "0.3.9"
 
 [deps]
 DualNumbers = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"

src/HypergeometricFunctions.jl

@@ -7,7 +7,7 @@ module HypergeometricFunctions
 
 using DualNumbers, LinearAlgebra, SpecialFunctions
 
-export _₁F₁, _₂F₁, _₃F₂, pFq
+export _₁F₁, _₂F₁, _₃F₂, pFq, positive₂F₁
 
 include("specialfunctions.jl")
 include("gauss.jl")

src/gauss.jl

@@ -64,6 +64,14 @@ function mxa_₂F₁(a, b, c, z)
     return (-z)^a*_₂F₁(a, b, c, z)
 end
 
+"""
+Compute the Gauss hypergeometric function `₂F₁(a, b; c; z)` with positive parameters a, b, and c and non-negative argument z. Useful for statisticians.
+"""
+function positive₂F₁(a, b, c, z)
+    @assert a > 0 && b > 0 && c > 0 && 0 ≤ z ≤ 1
+    return _₂F₁maclaurin(a, b, c, z)
+end
+
 """
 Compute the Gauss hypergeometric function `₂F₁(a, b; c; z)` with general parameters a, b, and c.
 This polyalgorithm is designed based on the paper