Start moving to SingularIntegrals.jl

.gitignore

@@ -1,2 +1,3 @@
 
 .DS_Store
+Manifest.toml

Project.toml

@@ -1,33 +1,12 @@
 name = "RiemannHilbert"
 uuid = "79305c5b-9889-52e9-bdbd-56f883c71fe0"
-version = "0.1"
+version = "0.1.0"
 
 [deps]
-ApproxFun = "28f2ccd6-bb30-5033-b560-165f7b14dc2f"
-ApproxFunBase = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
-ApproxFunFourier = "59844689-9c9d-51bf-9583-5b794ec66d30"
-ApproxFunOrthogonalPolynomials = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
-ApproxFunSingularities = "f8fcb915-6b99-5be2-b79a-d6dbef8e6e7e"
-DomainSets = "5b8099bc-c8ec-5219-889f-1d9e522a28bf"
-DualNumbers = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
-FastTransforms = "057dd010-8810-581a-b7be-e3fc3b93f78c"
-FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
-LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
-SingularIntegralEquations = "e094c991-5a90-5477-8896-c1e4c9552a1a"
-SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
-SpecialFunctions = "276daf66-3868-5448-9aa4-cd146d93841b"
-Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+ClassicalOrthogonalPolynomials = "b30e2e7b-c4ee-47da-9d5f-2c5c27239acd"
+PowerNumbers = "7635a310-babe-11e9-2fde-a3dff3ddcf26"
+SingularIntegrals = "d7440221-8b5e-42fc-909c-0567823f424a"
 
 [compat]
-ApproxFun = "0.11.8"
-ApproxFunBase = "0.2.3"
-ApproxFunFourier = "0.2"
-ApproxFunOrthogonalPolynomials = "0.3"
-ApproxFunSingularities = "0.1.6"
-DomainSets = "0.1"
-DualNumbers = "0.6"
-FastTransforms = "0.8"
-FillArrays = "0.6,0.7,0.8"
-SingularIntegralEquations = "0.6, 0.7"
-SpecialFunctions = "0.7,0.8,0.9"
-julia = "1.3"
+ClassicalOrthogonalPolynomials = "0.13.9"
+SingularIntegrals = "0.3.3"

examples/semiclassicalrhproblem.jl

@@ -0,0 +1,23 @@
+using SingularIntegrals, SemiclassicalOrthogonalPolynomials, ClassicalOrthogonalPolynomials
+
+P = SemiclassicalJacobi(2, 1/2, 0, 1/2)
+
+z = 1+im
+W = Weighted(Jacobi(0, 1/2))
+x = axes(W,1)
+@test (inv.(z .- x') * W)[3] ≈ stieltjes(W, z)[3] ≈ sum(W[:,3] ./ (z .- x))
+
+P = Jacobi(0, 1/2)
+W = Weighted(P)
+x = axes(W,1)
+@test (inv.(z .- x') * W)[3] ≈ stieltjes(W, z)[3]
+
+Y = (n,z) -> [Base.unsafe_getindex(P, z, n+1) stieltjes(W, z)[n+1]/(-2π*im)]
+
+w = JacobiWeight(0, 1/2)
+n = 5;  @test Y(n,0.1+0im) ≈  Y(n,0.1-0im) * [1 w[0.1]; 0 1]
+
+
+
+
+

src/LogNumber.jl

@@ -57,7 +57,7 @@ function exp(l::LogNumber)::ComplexF64
     end
 end
 
-# This is a relative version of dual number, in the sense that its realpart*(1+epsilon)
+# This is a relative version of dual number, in the sense that its realpart*(1+epsilon*ε)
 struct RiemannDual{T} <: Number
     realpart::T
     epsilon::T
@@ -141,7 +141,7 @@ end
 
 log1p(z::RiemannDual) = log(z+1)
 
-SingularIntegralEquations.HypergeometricFunctions.speciallog(x::RiemannDual) =
+HypergeometricFunctions.speciallog(x::RiemannDual) =
     (s = sqrt(x); 3(atanh(s)-realpart(s))/realpart(s)^3)