Complex Ultraspherical operators (#252)

* complex Ultraspherical operators

* version bump to v0.6.30

Author: jishnub

Project.toml

@@ -1,6 +1,6 @@
 name = "ApproxFunOrthogonalPolynomials"
 uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
-version = "0.6.29"
+version = "0.6.30"
 
 [deps]
 ApproxFunBase = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"

src/Spaces/Ultraspherical/UltrasphericalOperators.jl

@@ -13,7 +13,10 @@ recβ(::Type{T},S::Ultraspherical,k) where {T} = k/(2*(k-one(T)+order(S)))   # o
 recγ(::Type{T},S::Ultraspherical,k) where {T} = (k-2+2order(S))/(2*(k-one(T)+order(S)))   # one(T) ensures we get correct type
 
 
-normalization(::Type{T}, sp::Ultraspherical, k::Int) where T = (λ = order(sp); (T(2)^(1-2λ)*π)/((k+λ)*gamma(λ)^2*FastTransforms.Λ(T(k),one(λ),2λ)))
+function normalization(::Type{T}, sp::Ultraspherical, k::Int) where T
+    λ = order(sp)
+    T(2)^(1-2λ)*π/((k+λ)*gamma(λ)^2*FastTransforms.Λ(real(T(k)),one(λ),2λ))
+end
 
 ## Multiplication
 # these are special cases

test/UltrasphericalTest.jl

@@ -107,6 +107,13 @@ using HalfIntegers
                 @test g ≈ Fun(ff, Ultraspherical(n1))
             end
         end
+
+        @testset "complex normalization" begin
+            C = Conversion(NormalizedUltraspherical(NormalizedLegendre()), Ultraspherical(Legendre()))
+            CC = convert(Operator{ComplexF64}, C)
+            @test CC isa Operator{ComplexF64}
+            @test CC[1:4, 1:4] ≈ C[1:4, 1:4]
+        end
     end
 
     @testset "Normalized space" begin