Update test_hermite.jl

Author: dlfivefifty

test/test_hermite.jl

@@ -4,13 +4,20 @@ import DomainSets: ℝ
 
 @testset "Hermite" begin
     H = Hermite()
+    w = HermiteWeight()
+    
     @test axes(H) == (Inclusion(ℝ), oneto(∞))
     x = axes(H,1)
     @test H[0.1,1:4] ≈ [1,2*0.1,4*0.1^2-2,8*0.1^3-12*0.1]
+    @test w[0.1] ≈ exp(-0.1^2)
 
     X = jacobimatrix(H)
     @test 0.1 * H[0.1,1:10]' ≈ H[0.1,1:11]'*X[1:11,1:10]
 
+    @test (H'*(w .* H))[1,1] ≈ sqrt(π)
+    @test (H'*(w .* H))[2,2] ≈ 2sqrt(π)
+    @test (H'*(w .* H))[3,3] ≈ 8sqrt(π)
+
     D = Derivative(x)
     @test (D*H)[0.1,1:4] ≈ [0,2,8*0.1,24*0.1^2-12]
 end