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-rw-r--r--caselle_compare.nb858
-rw-r--r--schofield.wl26
2 files changed, 339 insertions, 545 deletions
diff --git a/caselle_compare.nb b/caselle_compare.nb
index 9172109..8ad80e6 100644
--- a/caselle_compare.nb
+++ b/caselle_compare.nb
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}, Open ]],
-Cell[41716, 972, 3620, 84, 125, "Input",ExpressionUUID->"34fe8bc4-abfb-4504-a7f1-045cd2a55ee6"],
Cell[CellGroupData[{
-Cell[45361, 1060, 212, 4, 22, "Input",ExpressionUUID->"40ec85df-7487-4ffe-afab-49583a090315"],
-Cell[45576, 1066, 476, 10, 25, "Output",ExpressionUUID->"f1acdb4d-a707-469d-887b-abc0e24714e7"]
+Cell[35000, 809, 3915, 87, 263, "Input",ExpressionUUID->"b7de9e01-4fea-49ea-97a1-b154bc61886b"],
+Cell[38918, 898, 1559, 42, 102, "Output",ExpressionUUID->"afaa9364-8f91-4950-979b-0f9ef86eab0e"]
}, Open ]],
-Cell[46067, 1079, 3789, 85, 122, "Input",ExpressionUUID->"b7de9e01-4fea-49ea-97a1-b154bc61886b"],
Cell[CellGroupData[{
-Cell[49881, 1168, 212, 4, 22, "Input",ExpressionUUID->"40438766-386e-4ef0-95c5-bb36288917ef"],
-Cell[50096, 1174, 735, 15, 44, "Output",ExpressionUUID->"462d7199-fbaa-4949-8313-776399b35c4a"]
+Cell[40514, 945, 212, 4, 29, "Input",ExpressionUUID->"40438766-386e-4ef0-95c5-bb36288917ef"],
+Cell[40729, 951, 735, 15, 99, "Output",ExpressionUUID->"462d7199-fbaa-4949-8313-776399b35c4a"]
}, Open ]],
Cell[CellGroupData[{
-Cell[50868, 1194, 4388, 128, 175, "Input",ExpressionUUID->"f81ed9c7-d940-4314-963c-c36ea0215ef3"],
-Cell[55259, 1324, 1199, 20, 60, "Output",ExpressionUUID->"2234af5e-068b-46a3-beaf-99a907ef5184"]
+Cell[41501, 971, 4388, 128, 493, "Input",ExpressionUUID->"f81ed9c7-d940-4314-963c-c36ea0215ef3"],
+Cell[45892, 1101, 1199, 20, 120, "Output",ExpressionUUID->"2234af5e-068b-46a3-beaf-99a907ef5184"]
}, Open ]],
Cell[CellGroupData[{
-Cell[56495, 1349, 882, 21, 41, "Input",ExpressionUUID->"dd088f15-420b-4212-8186-b62091ac9d6c"],
-Cell[57380, 1372, 435, 6, 25, "Output",ExpressionUUID->"21b5cf8e-7f0a-45f7-ab93-9e8ebe789a07"]
+Cell[47128, 1126, 882, 21, 113, "Input",ExpressionUUID->"dd088f15-420b-4212-8186-b62091ac9d6c"],
+Cell[48013, 1149, 435, 6, 25, "Output",ExpressionUUID->"21b5cf8e-7f0a-45f7-ab93-9e8ebe789a07"]
}, Open ]],
Cell[CellGroupData[{
-Cell[57852, 1383, 1195, 29, 41, "Input",ExpressionUUID->"e7fdb778-fd9a-4c13-95dc-aefbf5b8a29f"],
-Cell[59050, 1414, 349, 5, 25, "Output",ExpressionUUID->"a5e80f1a-5f57-4a7a-ad79-17c92282d141"]
+Cell[48485, 1160, 1195, 29, 41, "Input",ExpressionUUID->"e7fdb778-fd9a-4c13-95dc-aefbf5b8a29f"],
+Cell[49683, 1191, 349, 5, 25, "Output",ExpressionUUID->"a5e80f1a-5f57-4a7a-ad79-17c92282d141"]
}, Open ]],
Cell[CellGroupData[{
-Cell[59436, 1424, 228, 5, 22, "Input",ExpressionUUID->"feb08355-9ad1-4257-9f97-e394177d7e32"],
-Cell[59667, 1431, 274, 8, 25, "Output",ExpressionUUID->"87e29f54-9d68-4261-96d4-95d24dcdc36a"]
+Cell[50069, 1201, 228, 5, 22, "Input",ExpressionUUID->"feb08355-9ad1-4257-9f97-e394177d7e32"],
+Cell[50300, 1208, 274, 8, 25, "Output",ExpressionUUID->"87e29f54-9d68-4261-96d4-95d24dcdc36a"]
}, Open ]],
Cell[CellGroupData[{
-Cell[59978, 1444, 1542, 27, 55, "Input",ExpressionUUID->"e61ed118-a102-4290-8440-cba17b87145b"],
-Cell[61523, 1473, 12321, 270, 180, "Output",ExpressionUUID->"2e45389f-59c7-4eaf-9b3a-270214fa013e"]
+Cell[50611, 1221, 1542, 27, 55, "Input",ExpressionUUID->"e61ed118-a102-4290-8440-cba17b87145b"],
+Cell[52156, 1250, 12321, 270, 180, "Output",ExpressionUUID->"2e45389f-59c7-4eaf-9b3a-270214fa013e"]
}, Open ]],
-Cell[73859, 1746, 175, 3, 22, "Input",ExpressionUUID->"0f87aa05-2cc9-472a-ab27-39ee15777442"],
-Cell[74037, 1751, 356, 7, 24, "Input",ExpressionUUID->"627c17e0-e2d8-4347-8fe9-812183a42941"],
+Cell[64492, 1523, 175, 3, 22, "Input",ExpressionUUID->"0f87aa05-2cc9-472a-ab27-39ee15777442"],
+Cell[64670, 1528, 356, 7, 24, "Input",ExpressionUUID->"627c17e0-e2d8-4347-8fe9-812183a42941"],
Cell[CellGroupData[{
-Cell[74418, 1762, 176, 2, 22, "Input",ExpressionUUID->"f32c32be-7fcb-4660-bf43-cbc119acda96"],
-Cell[74597, 1766, 2097, 65, 77, "Output",ExpressionUUID->"01b48fb7-d8c9-4012-92f6-488cf7e7087c"]
+Cell[65051, 1539, 176, 2, 22, "Input",ExpressionUUID->"f32c32be-7fcb-4660-bf43-cbc119acda96"],
+Cell[65230, 1543, 2097, 65, 77, "Output",ExpressionUUID->"01b48fb7-d8c9-4012-92f6-488cf7e7087c"]
}, Open ]],
Cell[CellGroupData[{
-Cell[76731, 1836, 860, 24, 24, "Input",ExpressionUUID->"bfa6a31f-5eb9-4063-b798-e45ab1e3b53a"],
-Cell[77594, 1862, 1944, 57, 77, "Output",ExpressionUUID->"0ca79efb-1867-4b1f-96fc-4a691d54b72e"]
+Cell[67364, 1613, 860, 24, 24, "Input",ExpressionUUID->"bfa6a31f-5eb9-4063-b798-e45ab1e3b53a"],
+Cell[68227, 1639, 1944, 57, 77, "Output",ExpressionUUID->"0ca79efb-1867-4b1f-96fc-4a691d54b72e"]
}, Open ]],
Cell[CellGroupData[{
-Cell[79575, 1924, 2622, 77, 93, "Input",ExpressionUUID->"242aacdf-e4c7-423c-a26a-12188ba2476e"],
-Cell[82200, 2003, 21838, 439, 180, "Output",ExpressionUUID->"073d831e-11a6-4203-90ce-0df429c1a3f0"]
+Cell[70208, 1701, 2622, 77, 93, "Input",ExpressionUUID->"242aacdf-e4c7-423c-a26a-12188ba2476e"],
+Cell[72833, 1780, 21838, 439, 180, "Output",ExpressionUUID->"073d831e-11a6-4203-90ce-0df429c1a3f0"]
}, Open ]],
-Cell[104053, 2445, 725, 15, 24, "Input",ExpressionUUID->"80c6c675-eade-40e1-8d0f-13a6578b30ff"],
-Cell[104781, 2462, 764, 21, 22, "Input",ExpressionUUID->"d8847f2e-21fe-4fb7-84ae-676f83acdf5a"],
+Cell[94686, 2222, 725, 15, 24, "Input",ExpressionUUID->"80c6c675-eade-40e1-8d0f-13a6578b30ff"],
+Cell[95414, 2239, 764, 21, 22, "Input",ExpressionUUID->"d8847f2e-21fe-4fb7-84ae-676f83acdf5a"],
Cell[CellGroupData[{
-Cell[105570, 2487, 679, 17, 40, "Input",ExpressionUUID->"15d60f60-2f87-40da-a2c6-66d640111d75"],
-Cell[106252, 2506, 1298, 32, 44, "Output",ExpressionUUID->"6f1d902a-0431-4a99-adc2-97eb3c423317"]
+Cell[96203, 2264, 679, 17, 40, "Input",ExpressionUUID->"15d60f60-2f87-40da-a2c6-66d640111d75"],
+Cell[96885, 2283, 1298, 32, 44, "Output",ExpressionUUID->"6f1d902a-0431-4a99-adc2-97eb3c423317"]
}, Open ]],
Cell[CellGroupData[{
-Cell[107587, 2543, 736, 18, 57, "Input",ExpressionUUID->"bec4c929-c1a6-4fd0-be18-caf3643ba3a4"],
-Cell[108326, 2563, 14613, 314, 179, "Output",ExpressionUUID->"b48c9c3b-23cc-4864-8ea2-6e98855eb77d"]
+Cell[98220, 2320, 736, 18, 57, "Input",ExpressionUUID->"bec4c929-c1a6-4fd0-be18-caf3643ba3a4"],
+Cell[98959, 2340, 14613, 314, 179, "Output",ExpressionUUID->"b48c9c3b-23cc-4864-8ea2-6e98855eb77d"]
}, Open ]]
}
]
diff --git a/schofield.wl b/schofield.wl
index 98dc607..d3ad6d2 100644
--- a/schofield.wl
+++ b/schofield.wl
@@ -122,8 +122,20 @@ eqMid[F_, h_][m_] := D[
{θ, m} ] / m! /. θ -> 1
Φs = {
- -1.19773338379799339,
+ -Gamma[1/3]Gamma[1/5]Gamma[7/15]/(2 π Gamma[2/3]Gamma[4/5]Gamma[8/15])(4 π^2 Gamma[13/16]^2 Gamma[3/4]/(Gamma[3/16]^2 Gamma[1/4]))^(8/15),
-0.31881012489061,
+(*
+ Sin[π s(pp l - p k)/p]/Sin[π s/p(pp-p)](M π(ξ+1)Gamma[(2 ξ+2)/(3 ξ+6)]/(2^(2/3)Sqrt[3]Gamma[1/3]Gamma[ξ/(3 ξ+6)]))^(2 Δlk) Q[ξ, (ξ+1)l-ξ k] //. {
+ l -> 1, k -> 3, p -> 3, pp -> 4, ξ -> p/(pp-p), Δlk -> ((pp l-p k)^2-(pp-p)^2)/(4 p pp),
+ M -> 2^((ξ+5)/(3 ξ+6)) Sqrt[3] Gamma[1/3]Gamma[ξ/(3 ξ+6)]/π/Gamma[(2 ξ+2)/(3 ξ+6)](
+ π^2 Gamma[(3 ξ+4)/(4 ξ+4)]^2 Gamma[1/2+1/(ξ+1)]/Gamma[ξ/(4 ξ+4)]^2/Gamma[1/2-1/(ξ+1)]
+ )^((ξ+1)/(3 ξ + 6))
+ } /. Q -> Function[{ξ, η}, Exp[
+ NIntegrate[
+ (Sinh[(ξ+2)t]Sinh[t(η-1)]Sinh[t(η+1)]/Sinh[3(ξ+2)t]/Sinh[2(ξ+1)t]/Sinh[ξ t](Cosh[3(ξ+2)t]+Cosh[(ξ+4)t]-Cosh[(3 ξ+4)t]+Cosh[ξ t]+1)-(η^2-1)/(2 ξ(ξ+1))Exp[-4 t]) /t
+ ,{t, 0, Infinity}, WorkingPrecision->50]
+ ]],
+*)
Around[0.110886196683, 2.0 10^-12],
Around[0.01642689465, 1.0 10^-11],
Around[-2.639978 10^-4, 1.0 10^-10],
@@ -131,8 +143,8 @@ eqMid[F_, h_][m_] := D[
Around[2.08865 10^-4, 1.0 10^-9],
Around[-4.4819 10^-5, 1.0 10^-9],
Around[3.194 10^-7, 1.0 10^-9],
- 4.31 10^-6,
- -1.99 10^-6
+ Around[4.31 10^-6, 0.01 10^-6],
+ Around[-1.99 10^-6, 0.01 10^-6]
}
Gls = {
@@ -149,8 +161,8 @@ Gls = {
Around[-6.79 10^2, 1.0],
Around[5.34 10^3, 10.],
Around[-4.66 10^4, 0.01 10^4],
- 4.46 10^5,
- -4.66 10^6
+ Around[4.46 10^5, 0.01 10^5],
+ Around[-4.66 10^6, 0.01 10^6]
}
Ghs = {
@@ -166,9 +178,9 @@ Ghs = {
0,
Around[-2.5891 10^4, 2.0],
0,
- 5.02 10^5,
+ Around[5.02 10^5, 0.01 10^5],
0,
- -1.04 10^7
+ Around[-1.04 10^7, 0.01 10^7]
}
dRule[sym_][f_, i_] := Derivative[i[[1]] - 1][sym][0] -> f (i[[1]] - 1)!