close #68

Project.toml

@@ -1,6 +1,6 @@
 name = "HypergeometricFunctions"
 uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
-version = "0.3.21"
+version = "0.3.22"
 
 [deps]
 DualNumbers = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"

README.md

@@ -2,7 +2,7 @@
 
 [![Build Status](https://github.com/JuliaMath/HypergeometricFunctions.jl/workflows/CI/badge.svg)](https://github.com/JuliaMath/HypergeometricFunctions.jl/actions?query=workflow%3ACI) [![codecov](https://codecov.io/gh/JuliaMath/HypergeometricFunctions.jl/branch/master/graph/badge.svg)](https://codecov.io/gh/JuliaMath/HypergeometricFunctions.jl) [![](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaMath.github.io/HypergeometricFunctions.jl/stable) [![](https://img.shields.io/badge/docs-dev-blue.svg)](https://JuliaMath.github.io/HypergeometricFunctions.jl/dev)
 
-This package provides an implementation of the generalized hypergeometric function `pFq((α1,…,αp), (β1,…,βq), z)`.
+This package provides an implementation of the generalized hypergeometric function `pFq(α, β, z)`.
 
 ```julia
 julia> using HypergeometricFunctions

src/confluent.jl

@@ -1,7 +1,7 @@
 # The references to special cases are to NIST's DLMF.
 
 """
-Compute Kummer's confluent hypergeometric function `₁F₁(a, b; z)`.
+Compute Kummer's confluent hypergeometric function `₁F₁(a, b, z)`.
 """
 function _₁F₁(a, b, z; kwds...)
     z = float(z)
@@ -11,7 +11,7 @@ function _₁F₁(a, b, z; kwds...)
         if -a ∈ ℕ₀ && real(a) ≥ real(b)
             return _₁F₁maclaurin(a, b, z; kwds...)
         else
-            return throw(DomainError(b, "M(a, b, z) = ₁F₁(a; b; z) is not defined for negative integer b unless a is a nonpositive integer and a ≥ b."))
+            return throw(DomainError(b, "M(a, b, z) = ₁F₁(a, b, z) is not defined for negative integer b unless a is a nonpositive integer and a ≥ b."))
         end
     elseif -a ∈ ℕ₀
         return _₁F₁maclaurin(a, b, z; kwds...)
@@ -32,12 +32,12 @@ function _₁F₁general(a, b, z; kwds...)
 end
 
 """
-Compute Kummer's confluent hypergeometric function `M(a, b, z) = ₁F₁(a, b; z)`.
+Compute Kummer's confluent hypergeometric function `M(a, b, z) = ₁F₁(a, b, z)`.
 """
 const M = _₁F₁
 
 """
-Compute Tricomi's confluent hypergeometric function `U(a, b, z) ∼ z⁻ᵃ ₂F₀((a, a-b+1), (); -z⁻¹)`.
+Compute Tricomi's confluent hypergeometric function `U(a, b, z) ∼ z⁻ᵃ ₂F₀((a, a-b+1), (), -z⁻¹)`.
 """
 function U(a, b, z; kwds...)
     return z^-a*pFq((a, a-b+1), (), -inv(z); kwds...)

src/gauss.jl

@@ -1,7 +1,7 @@
 # The references to special cases are to Table of Integrals, Series, and Products, § 9.121, followed by NIST's DLMF.
 
 """
-Compute the Gauss hypergeometric function `₂F₁(a, b, c; z)`.
+Compute the Gauss hypergeometric function `₂F₁(a, b, c, z)`.
 """
 function _₂F₁(a, b, c, z; method::Symbol = :general, kwds...)
     z = float(z)
@@ -58,7 +58,7 @@ function _₂F₁(a, b, c, z; method::Symbol = :general, kwds...)
 end
 
 """
-Compute the Gauss hypergeometric function `₂F₁(a, b, c; z)` with positive parameters a, b, and c and argument 0 ≤ z ≤ 1. Useful for statisticians.
+Compute the Gauss hypergeometric function `₂F₁(a, b, c, z)` with positive parameters a, b, and c and argument 0 ≤ z ≤ 1. Useful for statisticians.
 """
 function _₂F₁positive(a, b, c, z; kwds...)
     @assert a > 0 && b > 0 && c > 0 && 0 ≤ z ≤ 1
@@ -70,7 +70,7 @@ function _₂F₁positive(a, b, c, z; kwds...)
 end
 
 """
-Compute the Gauss hypergeometric function `₂F₁(a, b, c; z)` with general parameters a, b, and c.
+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
 
 > N. Michel and M. V. Stoitsov, [Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Pöschl–Teller–Ginocchio potential wave functions](https://doi.org/10.1016/j.cpc.2007.11.007), *Comp. Phys. Commun.*, **178**:535–551, 2008.
@@ -100,7 +100,7 @@ function _₂F₁general(a, b, c, z; kwds...)
 end
 
 """
-Compute the Gauss hypergeometric function `₂F₁(a, b, c; z)` with general parameters a, b, and c.
+Compute the Gauss hypergeometric function `₂F₁(a, b, c, z)` with general parameters a, b, and c.
 This polyalgorithm is designed based on the review
 
 > J. W. Pearson, S. Olver and M. A. Porter, [Numerical methods for the computation of the confluent and Gauss hypergeometric functions](https://doi.org/10.1007/s11075-016-0173-0), *Numer. Algor.*, **74**:821–866, 2017.

src/generalized.jl

@@ -1,8 +1,8 @@
 @doc raw"""
-    pFq(α, β; z)
+    pFq(α, β, z)
 Compute the generalized hypergeometric function, defined by
 ```math
-{}_pF_q(α, β; z) = \sum_{k=0}^\infty \dfrac{(\alpha_1)_k\cdots(\alpha_p)_k}{(\beta_1)_k\cdots(\beta_q)_k}\dfrac{z^k}{k!},
+{}_pF_q(α, β, z) = \sum_{k=0}^\infty \dfrac{(\alpha_1)_k\cdots(\alpha_p)_k}{(\beta_1)_k\cdots(\beta_q)_k}\dfrac{z^k}{k!},
 ```
 where the series converges and elsewhere by analytic continuation.
 
@@ -79,7 +79,7 @@ end
 pFq(α::AbstractVector, β::AbstractVector, z; kwds...) = pFq(Tuple(α), Tuple(β), z; kwds...)
 
 """
-Compute the generalized hypergeometric function `pFq(α, β; z)` by continued fraction.
+Compute the generalized hypergeometric function `pFq(α, β, z)` by continued fraction.
 """
 function pFqcontinuedfraction(α::AbstractVector{S}, β::AbstractVector{U}, z::V) where {S, U, V}
     T = promote_type(S, U, V)
@@ -91,7 +91,7 @@ function pFqcontinuedfraction(α::AbstractVector{S}, β::AbstractVector{U}, z::V
 end
 
 """
-Compute the generalized hypergeometric function `₃F₂(a₁, 1, 1, b₁, 2; z)`.
+Compute the generalized hypergeometric function `₃F₂(a₁, 1, 1, b₁, 2, z)`.
 """
 _₃F₂(a₁, b₁, z; kwds...) = _₃F₂(a₁, 1, 1, b₁, 2, z; kwds...)
 """

src/specialfunctions.jl

@@ -348,9 +348,10 @@ function Aone(a, b, c, w, m::Int, ϵ)
 end
 
 function Bone(a, b, c, w, m::Int, ϵ)
+    T = promote_type(typeof(a), typeof(b), typeof(c), typeof(w), typeof(m), typeof(ϵ))
     βₙ, γₙ = reconeβ₀(a, b, c, w, m, ϵ)*one(w), reconeγ₀(a, b, c, w, m, ϵ)*w
     ret, n = βₙ, 0
-    while abs(βₙ) > 8abs(ret)*eps() || n ≤ 0
+    while abs(βₙ) > 8abs(ret)*eps(real(T)) || n ≤ 0
         βₙ = (a+m+n+ϵ)*(b+m+n+ϵ)/((m+n+1+ϵ)*(n+1))*w*βₙ + ( (a+m+n)*(b+m+n)/(m+n+1) - (a+m+n) - (b+m+n) - ϵ + (a+m+n+ϵ)*(b+m+n+ϵ)/(n+1) )*γₙ/((m+n+1+ϵ)*(n+1-ϵ))
         ret += βₙ
         γₙ *= (a+m+n)*(b+m+n)/((m+n+1)*(n+1-ϵ))*w
@@ -412,10 +413,11 @@ function AInf(a, b, c, w, m::Int, ϵ)
 end
 
 function BInf(a, b, c, win, m::Int, ϵ)
+    T = promote_type(typeof(a), typeof(b), typeof(c), typeof(win), typeof(m), typeof(ϵ))
     w = win
     βₙ, γₙ = recInfβ₀(a, b, c, win, m, ϵ)*one(w), recInfγ₀(a, b, c, win, m, ϵ)*w
     ret, n = βₙ, 0
-    while abs(βₙ) > 8abs(ret)*eps() || n ≤ 0
+    while abs(βₙ) > 8abs(ret)*eps(real(T)) || n ≤ 0
         βₙ = (a+m+n+ϵ)*(1-c+a+m+n+ϵ)/((m+n+1+ϵ)*(n+1))*w*βₙ + ( (a+m+n)*(1-c+a+m+n)/(m+n+1) - (a+m+n) - (1-c+a+m+n) - ϵ + (a+m+n+ϵ)*(1-c+a+m+n+ϵ)/(n+1) )*γₙ/((m+n+1+ϵ)*(n+1-ϵ))
         ret += βₙ
         γₙ *= (a+m+n)*(1-c+a+m+n)/((m+n+1)*(n+1-ϵ))*w
@@ -555,7 +557,7 @@ function pFqmaclaurin(a::NTuple{p, S}, b::NTuple{q, U}, z::V; kmax::Int = KMAX)
         S₀, S₁ = S₁, S₁+(S₁-S₀)*rₖ
         k += 1
     end
-    k < kmax || @warn "Maclaurin approximation to "*pFq2string(Val{p}(), Val{q}())*" reached the maximum degree of "*string(kmax)*"."
+    k < kmax || @warn "Maclaurin approximation to "*pFq2string(Val(p), Val(q))*" reached the maximum degree of "*string(kmax)*"."
     return S₁
 end