update Manifest

Manifest.toml

@@ -1,20 +1,46 @@
+# This file is machine-generated - editing it directly is not advised
+
 [[AbstractFFTs]]
-deps = ["LinearAlgebra", "Test"]
-git-tree-sha1 = "dfaf23dba016254bb0eed6de326510caea2889bf"
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "380e36c66edfa099cd90116b24c1ce8cafccac40"
 uuid = "621f4979-c628-5d54-868e-fcf4e3e8185c"
-version = "0.4.0"
+version = "0.4.1"
 
 [[ApproxFun]]
-deps = ["AbstractFFTs", "BandedMatrices", "BlockArrays", "BlockBandedMatrices", "Calculus", "DSP", "DomainSets", "DualNumbers", "FFTW", "FastGaussQuadrature", "FastTransforms", "FillArrays", "InfiniteArrays", "IntervalSets", "LazyArrays", "LinearAlgebra", "LowRankApprox", "Random", "RecipesBase", "SparseArrays", "SpecialFunctions", "StaticArrays", "Statistics", "Test", "ToeplitzMatrices"]
-git-tree-sha1 = "2fbd592ab81eec53b7f256e771507a10ae38a3e6"
+deps = ["AbstractFFTs", "ApproxFunBase", "ApproxFunFourier", "ApproxFunOrthogonalPolynomials", "ApproxFunSingularities", "BandedMatrices", "BlockArrays", "BlockBandedMatrices", "Calculus", "DSP", "DomainSets", "DualNumbers", "FFTW", "FastGaussQuadrature", "FastTransforms", "FillArrays", "InfiniteArrays", "IntervalSets", "LazyArrays", "LinearAlgebra", "LowRankApprox", "Random", "RecipesBase", "Reexport", "SparseArrays", "SpecialFunctions", "StaticArrays", "Test", "ToeplitzMatrices"]
+git-tree-sha1 = "e960d8b4a1e9762576a14a41bcf06a8e8a832f81"
 uuid = "28f2ccd6-bb30-5033-b560-165f7b14dc2f"
-version = "0.10.4"
+version = "0.11.1"
+
+[[ApproxFunBase]]
+deps = ["AbstractFFTs", "BandedMatrices", "BlockArrays", "BlockBandedMatrices", "Calculus", "DSP", "DomainSets", "DualNumbers", "FFTW", "FastGaussQuadrature", "FastTransforms", "FillArrays", "InfiniteArrays", "IntervalSets", "LazyArrays", "LinearAlgebra", "LowRankApprox", "Random", "SparseArrays", "SpecialFunctions", "StaticArrays", "Statistics", "Test", "ToeplitzMatrices"]
+git-tree-sha1 = "295188399d5be7a5fbb17715ef6fdda481bdbdbc"
+uuid = "fbd15aa5-315a-5a7d-a8a4-24992e37be05"
+version = "0.1.1"
+
+[[ApproxFunFourier]]
+deps = ["AbstractFFTs", "ApproxFunBase", "BandedMatrices", "BlockArrays", "BlockBandedMatrices", "Calculus", "DSP", "DomainSets", "DualNumbers", "FFTW", "FastGaussQuadrature", "FastTransforms", "FillArrays", "InfiniteArrays", "IntervalSets", "LazyArrays", "LinearAlgebra", "LowRankApprox", "Reexport", "SpecialFunctions", "StaticArrays", "Test", "ToeplitzMatrices"]
+git-tree-sha1 = "6176bbfc78819197219bc90e7068bc97b953df03"
+uuid = "59844689-9c9d-51bf-9583-5b794ec66d30"
+version = "0.1.1"
+
+[[ApproxFunOrthogonalPolynomials]]
+deps = ["AbstractFFTs", "ApproxFunBase", "BandedMatrices", "BlockArrays", "BlockBandedMatrices", "Calculus", "DSP", "DomainSets", "DualNumbers", "FFTW", "FastGaussQuadrature", "FastTransforms", "FillArrays", "InfiniteArrays", "IntervalSets", "LazyArrays", "LinearAlgebra", "LowRankApprox", "Reexport", "SpecialFunctions", "StaticArrays", "Statistics", "Test", "ToeplitzMatrices"]
+git-tree-sha1 = "5ab39aa163af72352ab51dd9354298dd45351564"
+uuid = "b70543e2-c0d9-56b8-a290-0d4d6d4de211"
+version = "0.1.1"
+
+[[ApproxFunSingularities]]
+deps = ["AbstractFFTs", "ApproxFunBase", "ApproxFunOrthogonalPolynomials", "BandedMatrices", "BlockArrays", "BlockBandedMatrices", "Calculus", "DSP", "DomainSets", "DualNumbers", "FFTW", "FastGaussQuadrature", "FastTransforms", "FillArrays", "InfiniteArrays", "IntervalSets", "LazyArrays", "LinearAlgebra", "LowRankApprox", "Random", "Reexport", "SpecialFunctions", "StaticArrays", "Statistics", "Test", "ToeplitzMatrices"]
+git-tree-sha1 = "8946ecaa528ce34c6a48625c40523e10ac6b9540"
+uuid = "f8fcb915-6b99-5be2-b79a-d6dbef8e6e7e"
+version = "0.1.0"
 
 [[BandedMatrices]]
 deps = ["FillArrays", "LazyArrays", "LinearAlgebra", "MatrixFactorizations", "Random", "SparseArrays", "Test"]
-git-tree-sha1 = "1249cc93e4a685e8f0aaf1aa858fdd636551c754"
+git-tree-sha1 = "dd74592d0952af59b97e12d6f69bfc9cc3a79614"
 uuid = "aae01518-5342-5314-be14-df237901396f"
-version = "0.9.0"
+version = "0.9.2"
 
 [[Base64]]
 uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
@@ -26,28 +52,28 @@ uuid = "9e28174c-4ba2-5203-b857-d8d62c4213ee"
 version = "0.8.10"
 
 [[BinaryProvider]]
-deps = ["Libdl", "Pkg", "SHA", "Test"]
-git-tree-sha1 = "055eb2690182ebc31087859c3dd8598371d3ef9e"
+deps = ["Libdl", "SHA"]
+git-tree-sha1 = "c7361ce8a2129f20b0e05a89f7070820cfed6648"
 uuid = "b99e7846-7c00-51b0-8f62-c81ae34c0232"
-version = "0.5.3"
+version = "0.5.4"
 
 [[BlockArrays]]
-deps = ["Base64", "LinearAlgebra", "SparseArrays", "Test"]
-git-tree-sha1 = "68a477c2f2ddbbe518dc31a42aaf2df38bdfd93c"
+deps = ["LinearAlgebra"]
+git-tree-sha1 = "a36887ddaaf66b8f5bd017871f239247aa6f459f"
 uuid = "8e7c35d0-a365-5155-bbbb-fb81a777f24e"
-version = "0.7.0"
+version = "0.9.1"
 
 [[BlockBandedMatrices]]
-deps = ["BandedMatrices", "BlockArrays", "Distributed", "FillArrays", "LazyArrays", "LinearAlgebra", "Pkg", "Profile", "Random", "SharedArrays", "SparseArrays", "Statistics", "Test"]
-git-tree-sha1 = "51536cbbc652df93b85861139b6536c81096011d"
+deps = ["BandedMatrices", "BlockArrays", "Distributed", "FillArrays", "LazyArrays", "LinearAlgebra", "MatrixFactorizations", "Pkg", "Profile", "Random", "SharedArrays", "SparseArrays", "Statistics", "Test"]
+git-tree-sha1 = "a7406aeb0778742e7c728bea69fb23d4966fa9d6"
 uuid = "ffab5731-97b5-5995-9138-79e8c1846df0"
-version = "0.3.4"
+version = "0.4.4"
 
 [[CSTParser]]
-deps = ["LibGit2", "Test", "Tokenize"]
-git-tree-sha1 = "437c93bc191cd55957b3f8dee7794b6131997c56"
+deps = ["Tokenize"]
+git-tree-sha1 = "376a39f1862000442011390f1edf5e7f4dcc7142"
 uuid = "00ebfdb7-1f24-5e51-bd34-a7502290713f"
-version = "0.5.2"
+version = "0.6.0"
 
 [[Calculus]]
 deps = ["Compat"]
@@ -68,10 +94,10 @@ uuid = "34da2185-b29b-5c13-b0c7-acf172513d20"
 version = "2.1.0"
 
 [[Conda]]
-deps = ["Compat", "JSON", "VersionParsing"]
-git-tree-sha1 = "b625d802587c2150c279a40a646fba63f9bd8187"
+deps = ["JSON", "VersionParsing"]
+git-tree-sha1 = "9a11d428dcdc425072af4aea19ab1e8c3e01c032"
 uuid = "8f4d0f93-b110-5947-807f-2305c1781a2d"
-version = "1.2.0"
+version = "1.3.0"
 
 [[DSP]]
 deps = ["AbstractFFTs", "Compat", "FFTW", "LinearAlgebra", "Polynomials", "Random", "Reexport", "SpecialFunctions"]
@@ -94,10 +120,10 @@ deps = ["Mmap"]
 uuid = "8bb1440f-4735-579b-a4ab-409b98df4dab"
 
 [[DiffEqDiffTools]]
-deps = ["LinearAlgebra", "Test"]
-git-tree-sha1 = "30f82c63cb9d293513b360572e283c19577fcf82"
+deps = ["LinearAlgebra", "SparseArrays", "StaticArrays"]
+git-tree-sha1 = "c83f4ce45d4b723f9d21b9ea3d314a503fd40def"
 uuid = "01453d9d-ee7c-5054-8395-0335cb756afa"
-version = "0.8.1"
+version = "0.12.0"
 
 [[DiffResults]]
 deps = ["Compat", "StaticArrays"]
@@ -112,14 +138,14 @@ uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
 version = "0.0.10"
 
 [[Distributed]]
-deps = ["LinearAlgebra", "Random", "Serialization", "Sockets"]
+deps = ["Random", "Serialization", "Sockets"]
 uuid = "8ba89e20-285c-5b6f-9357-94700520ee1b"
 
 [[DomainSets]]
 deps = ["IntervalSets", "LinearAlgebra", "StaticArrays", "Statistics", "Test"]
-git-tree-sha1 = "84beb94a9595c1a7a692880b424f82470a326976"
+git-tree-sha1 = "8172e0bf793c497fd23990281a800379000182bc"
 uuid = "5b8099bc-c8ec-5219-889f-1d9e522a28bf"
-version = "0.0.1"
+version = "0.0.2"
 
 [[DualNumbers]]
 deps = ["Calculus", "LinearAlgebra", "NaNMath", "SpecialFunctions", "Test"]
@@ -141,15 +167,15 @@ version = "0.3.3"
 
 [[FastTransforms]]
 deps = ["AbstractFFTs", "Compat", "DSP", "FFTW", "HierarchicalMatrices", "LinearAlgebra", "LowRankApprox", "ProgressMeter", "SpecialFunctions", "ToeplitzMatrices"]
-git-tree-sha1 = "051b635520e679c8c72aa43a40d86e2c226bbb7f"
+git-tree-sha1 = "f7f912b0f00cdf5b4632c840aa7954be0de4b965"
 uuid = "057dd010-8810-581a-b7be-e3fc3b93f78c"
-version = "0.4.2"
+version = "0.5.0"
 
 [[FillArrays]]
 deps = ["LinearAlgebra", "Random", "SparseArrays", "Test"]
-git-tree-sha1 = "2def0123a4f3572234405b0e3d80bfe5d3e1a2a4"
+git-tree-sha1 = "9ab8f76758cbabba8d7f103c51dce7f73fcf8e92"
 uuid = "1a297f60-69ca-5386-bcde-b61e274b549b"
-version = "0.5.0"
+version = "0.6.3"
 
 [[ForwardDiff]]
 deps = ["CommonSubexpressions", "DiffResults", "DiffRules", "InteractiveUtils", "LinearAlgebra", "NaNMath", "Random", "SparseArrays", "SpecialFunctions", "StaticArrays", "Test"]
@@ -165,12 +191,12 @@ version = "0.1.4"
 
 [[InfiniteArrays]]
 deps = ["DSP", "FillArrays", "LazyArrays", "LinearAlgebra", "SparseArrays", "Statistics", "Test"]
-git-tree-sha1 = "ceb060a732135d83d75f4b4059374d9d35e27b03"
+git-tree-sha1 = "70638fa3691bf61bcfdca471d3b3a047b418bc04"
 uuid = "4858937d-0d70-526a-a4dd-2d5cb5dd786c"
-version = "0.0.3"
+version = "0.1.1"
 
 [[InteractiveUtils]]
-deps = ["LinearAlgebra", "Markdown"]
+deps = ["Markdown"]
 uuid = "b77e0a4c-d291-57a0-90e8-8db25a27a240"
 
 [[IntervalSets]]
@@ -187,9 +213,9 @@ version = "0.20.0"
 
 [[LazyArrays]]
 deps = ["FillArrays", "LinearAlgebra", "MacroTools", "StaticArrays", "Test"]
-git-tree-sha1 = "4439e840fe68cbcde806fcc625d05166227a56a5"
+git-tree-sha1 = "5eec856c454496abe8f4504227fcc187205a502a"
 uuid = "5078a376-72f3-5289-bfd5-ec5146d43c02"
-version = "0.8.0"
+version = "0.9.0"
 
 [[LibGit2]]
 uuid = "76f85450-5226-5b5a-8eaa-529ad045b433"
@@ -212,9 +238,9 @@ uuid = "56ddb016-857b-54e1-b83d-db4d58db5568"
 
 [[LowRankApprox]]
 deps = ["FFTW", "FillArrays", "LinearAlgebra", "Nullables", "Random", "SparseArrays", "Test"]
-git-tree-sha1 = "dd7586356fe6bc41057ee5082487c90f6790b339"
+git-tree-sha1 = "4079dfefba2cf541e0770e6426f7756ee90efbe8"
 uuid = "898213cb-b102-5a47-900c-97e73b919f73"
-version = "0.2.2"
+version = "0.2.3"
 
 [[MacroTools]]
 deps = ["CSTParser", "Compat", "DataStructures", "Test"]
@@ -233,10 +259,10 @@ uuid = "a3b82374-2e81-5b9e-98ce-41277c0e4c87"
 version = "0.0.4"
 
 [[Missings]]
-deps = ["Dates", "InteractiveUtils", "SparseArrays", "Test"]
-git-tree-sha1 = "d1d2585677f2bd93a97cfeb8faa7a0de0f982042"
+deps = ["SparseArrays", "Test"]
+git-tree-sha1 = "f0719736664b4358aa9ec173077d4285775f8007"
 uuid = "e1d29d7a-bbdc-5cf2-9ac0-f12de2c33e28"
-version = "0.4.0"
+version = "0.4.1"
 
 [[Mmap]]
 uuid = "a63ad114-7e13-5084-954f-fe012c677804"
@@ -260,10 +286,9 @@ uuid = "4d1e1d77-625e-5b40-9113-a560ec7a8ecd"
 version = "0.0.8"
 
 [[OffsetArrays]]
-deps = ["DelimitedFiles", "Test"]
-git-tree-sha1 = "e6893807f09c1d5517861ded8b203cb96cb7d44a"
+git-tree-sha1 = "1af2f79c7eaac3e019a0de41ef63335ff26a0a57"
 uuid = "6fe1bfb0-de20-5000-8ca7-80f57d26f881"
-version = "0.10.0"
+version = "0.11.1"
 
 [[Optim]]
 deps = ["Calculus", "DiffEqDiffTools", "ForwardDiff", "LineSearches", "LinearAlgebra", "NLSolversBase", "NaNMath", "Parameters", "PositiveFactorizations", "Printf", "Random", "SparseArrays", "StatsBase", "Test"]
@@ -295,9 +320,9 @@ version = "0.5.2"
 
 [[PositiveFactorizations]]
 deps = ["LinearAlgebra", "Test"]
-git-tree-sha1 = "86ae7329c4b5c266acf5c7c524a972300d991e1c"
+git-tree-sha1 = "957c3dd7c33895469760ce873082fbb6b3620641"
 uuid = "85a6dd25-e78a-55b7-8502-1745935b8125"
-version = "0.2.1"
+version = "0.2.2"
 
 [[Printf]]
 deps = ["Unicode"]
@@ -308,10 +333,10 @@ deps = ["Printf"]
 uuid = "9abbd945-dff8-562f-b5e8-e1ebf5ef1b79"
 
 [[ProgressMeter]]
-deps = ["Distributed", "Printf", "Random", "Test"]
-git-tree-sha1 = "48058bc11607676e5bbc0b974af79106c6200787"
+deps = ["Distributed", "Printf"]
+git-tree-sha1 = "0f08e0e74e5b160ca20d3962a2620038b75881c7"
 uuid = "92933f4c-e287-5a05-a399-4b506db050ca"
-version = "0.9.0"
+version = "1.0.0"
 
 [[REPL]]
 deps = ["InteractiveUtils", "Markdown", "Sockets"]
@@ -322,10 +347,9 @@ deps = ["Serialization"]
 uuid = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 
 [[RecipesBase]]
-deps = ["Random", "Test"]
-git-tree-sha1 = "0b3cb370ee4dc00f47f1193101600949f3dcf884"
+git-tree-sha1 = "7bdce29bc9b2f5660a6e5e64d64d91ec941f6aa2"
 uuid = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
-version = "0.6.0"
+version = "0.7.0"
 
 [[Reexport]]
 deps = ["Pkg"]
@@ -363,20 +387,20 @@ uuid = "276daf66-3868-5448-9aa4-cd146d93841b"
 version = "0.7.2"
 
 [[StaticArrays]]
-deps = ["InteractiveUtils", "LinearAlgebra", "Random", "Statistics", "Test"]
-git-tree-sha1 = "3841b39ed5f047db1162627bf5f80a9cd3e39ae2"
+deps = ["LinearAlgebra", "Random", "Statistics"]
+git-tree-sha1 = "db23bbf50064c582b6f2b9b043c8e7e98ea8c0c6"
 uuid = "90137ffa-7385-5640-81b9-e52037218182"
-version = "0.10.3"
+version = "0.11.0"
 
 [[Statistics]]
 deps = ["LinearAlgebra", "SparseArrays"]
 uuid = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 
 [[StatsBase]]
-deps = ["DataStructures", "DelimitedFiles", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics", "Test"]
-git-tree-sha1 = "435707791dc85a67d98d671c1c3fcf1b20b00f94"
+deps = ["DataStructures", "LinearAlgebra", "Missings", "Printf", "Random", "SortingAlgorithms", "SparseArrays", "Statistics"]
+git-tree-sha1 = "8a0f4b09c7426478ab677245ab2b0b68552143c7"
 uuid = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
-version = "0.29.0"
+version = "0.30.0"
 
 [[Test]]
 deps = ["Distributed", "InteractiveUtils", "Logging", "Random"]
@@ -389,10 +413,9 @@ uuid = "c751599d-da0a-543b-9d20-d0a503d91d24"
 version = "0.5.0"
 
 [[Tokenize]]
-deps = ["Printf", "Test"]
-git-tree-sha1 = "3e83f60b74911d3042d3550884ca2776386a02b8"
+git-tree-sha1 = "0de343efc07da00cd449d5b04e959ebaeeb3305d"
 uuid = "0796e94c-ce3b-5d07-9a54-7f471281c624"
-version = "0.5.3"
+version = "0.5.4"
 
 [[URIParser]]
 deps = ["Test", "Unicode"]
@@ -401,7 +424,7 @@ uuid = "30578b45-9adc-5946-b283-645ec420af67"
 version = "0.4.0"
 
 [[UUIDs]]
-deps = ["Random"]
+deps = ["Random", "SHA"]
 uuid = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
 [[Unicode]]

Project.toml

@@ -19,4 +19,4 @@ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["LinearAlgebra","Test"]
+test = ["LinearAlgebra", "Test"]

test/specialfunctions.jl

@@ -3,7 +3,11 @@
     @test sbesselj(1, x) ≈ sin(x)/x^2 - cos(x)/x
     @test shankelh1(1, x) ≈ - exp(im*x) * (x + im) / (x^2)
 
-    @test shankelh1(1, x) ≈ - exp(im*x) * (x + im) / (x^2)
+    x = 3.1 + 1.1im
+    n = 1
     @test 2 * diffsbessel(shankelh1,n,x) ≈ shankelh1(n-1, x) - (shankelh1(n, x) + x*shankelh1(n+1, x))/x
 
+    x = 3.1 - 2.1im
+    n = 2
+    @test 2 * diffsbessel(shankelh1,n,x) ≈ shankelh1(n-1, x) - (shankelh1(n, x) + x*shankelh1(n+1, x))/x
 end