Legendre and weighted Ultraspherical (#165)

Author: dlfivefifty

Project.toml

@@ -1,7 +1,7 @@
 name = "ClassicalOrthogonalPolynomials"
 uuid = "b30e2e7b-c4ee-47da-9d5f-2c5c27239acd"
 authors = ["Sheehan Olver <[email protected]>"]
-version = "0.12.1"
+version = "0.12.2"
 
 [deps]
 ArrayLayouts = "4c555306-a7a7-4459-81d9-ec55ddd5c99a"

src/classical/ultraspherical.jl

@@ -153,6 +153,7 @@ end
 
 \(A::Ultraspherical, B::Legendre) = A\Ultraspherical(B)
 \(A::Legendre, B::Ultraspherical) = Ultraspherical(A)\B
+\(A::Legendre, B::Weighted{<:Any,<:Ultraspherical}) = Weighted(Ultraspherical(A))\B
 
 function \(A::Ultraspherical, B::Jacobi)
     Ã = Jacobi(A)

test/test_ultraspherical.jl

@@ -168,4 +168,12 @@ using ClassicalOrthogonalPolynomials: grammatrix
         W = Weighted(T) \ diff(Weighted(Ultraspherical(1)))
         @test W[1:10,1:10] == diagm(-1 => -(1:9))
     end
+
+    @testset "Legendre" begin
+        P = Legendre()
+        P̃ = Ultraspherical(1/2)
+        C = Ultraspherical(3/2)
+        @test P[0.1,1:5] ≈ P̃[0.1,1:5] 
+        @test (P \ Weighted(C))[1:10,1:10] ≈ (P \ Weighted(Jacobi(1,1)))[1:10,1:10] * (Jacobi(1,1) \ C)[1:10,1:10]
+    end
 end