fix jacobi normalization for complex T (#229)

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunOrthogonalPolynomials"
 uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
-version = "0.6.22"
+version = "0.6.23"
 
 [deps]
 ApproxFunBase = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"

src/Spaces/Jacobi/Jacobi.jl

@@ -23,16 +23,17 @@ NormalizedJacobi(s...) = NormalizedPolynomialSpace(Jacobi(s...))
 NormalizedLegendre(d...) = NormalizedPolynomialSpace(Legendre(d...))
 
 function normalization(::Type{T}, sp::Jacobi, k::Int) where T
+    x = FastTransforms.Anαβ(k, sp.a, sp.b)
     if sp.a == sp.b == -0.5 && k == 0
         # In this case, the expression for Anαβ has a division by zero, so we evaluate this using Mathematica
         # In principle this may be generalized to arbitrary α + β = -1
         # The exact expression from Mathematica in terms of the hypergeometric 2F1 function
         # \fbox{$\frac{\, _2F_1(1,-\alpha ;\beta +2;-1)}{\beta +1}+\frac{\, _2F_1(1,-\beta ;\alpha +2;-1)}{\alpha +1}\text{ if }\alpha >-1\land \beta >-1$}
         # or, by eliminating β and expressed in terms of the polygamma function,
         # \fbox{$\frac{1}{2} \left(\psi ^{(0)}\left(\frac{1}{2}-\frac{\alpha }{2}\right)-\psi ^{(0)}\left(-\frac{\alpha }{2}\right)\right)+\frac{1}{2} \left(\psi ^{(0)}\left(\frac{\alpha }{2}+1\right)-\psi ^{(0)}\left(\frac{\alpha }{2}+\frac{1}{2}\right)\right)\text{ if }-1<\alpha <0$}
-        T(pi)
+        oftype(x, pi)
     else
-        FastTransforms.Anαβ(T(k), T(sp.a), T(sp.b))
+        x
     end
 end
 

test/JacobiTest.jl

@@ -192,6 +192,8 @@ using Static
                     NormalizedUltraspherical(NormalizedPolynomialSpace(j))
             end
         end
+
+        @test ApproxFunOrthogonalPolynomials.normalization(ComplexF64, Jacobi(-0.5, -0.5), 0) ≈ pi
     end
 
     @testset "inplace transform" begin