close #69

This excludes the case where the 3-term recurrence collapses to a 2-term recurrence. This was caught by a previous test, so a specific test is added

Author: MikaelSlevinsky

Project.toml

@@ -1,6 +1,6 @@
 name = "HypergeometricFunctions"
 uuid = "34004b35-14d8-5ef3-9330-4cdb6864b03a"
-version = "0.3.22"
+version = "0.3.23"
 
 [deps]
 DualNumbers = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"

src/gauss.jl

@@ -149,7 +149,7 @@ function _₂F₁general2(a, b, c, z; kwds...)
     elseif abs(z-0.5) > 0.5
         if isapprox(a, b) && !isapprox(c, a+0.5)
             return gamma(c)/gamma(a)/gamma(c-a)*(0.5-z)^(-a)*_₂F₁continuationalt(a, c, 0.5, z; kwds...)
-        elseif a-b ∉ ℤ
+        elseif a-b ∉ ℤ && !isapprox(2c, a+b+1)
             return gamma(c)*(gamma(b-a)/gamma(b)/gamma(c-a)*(0.5-z)^(-a)*_₂F₁continuation(a, a+b, c, 0.5, z; kwds...) + gamma(a-b)/gamma(a)/gamma(c-b)*(0.5-z)^(-b)*_₂F₁continuation(b, a+b, c, 0.5, z; kwds...))
         end
     end

test/runtests.jl

@@ -63,6 +63,7 @@ end
                 j += 1
             end
         end
+        @test _₂F₁general(-0.4, 0.4, 0.5, 0.75+0.75im) ≈ _₂F₁general2(-0.4, 0.4, 0.5, 0.75+0.75im)
     end
 
     @testset "Test that _₂F₁ is inferred for Float32 arguments" begin