Coefficient updates.

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
@@ -10,10 +10,10 @@
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 }, Open  ]],
 Cell[CellGroupData[{
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 Cell[CellGroupData[{
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 Cell[CellGroupData[{
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+Cell[30619, 702, 3652, 83, 247, "Input",ExpressionUUID->"34fe8bc4-abfb-4504-a7f1-045cd2a55ee6"],
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 Cell[CellGroupData[{
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+Cell[35000, 809, 3915, 87, 263, "Input",ExpressionUUID->"b7de9e01-4fea-49ea-97a1-b154bc61886b"],
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-Cell[46067, 1079, 3789, 85, 122, "Input",ExpressionUUID->"b7de9e01-4fea-49ea-97a1-b154bc61886b"],
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+Cell[40514, 945, 212, 4, 29, "Input",ExpressionUUID->"40438766-386e-4ef0-95c5-bb36288917ef"],
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 Cell[CellGroupData[{
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-Cell[57380, 1372, 435, 6, 25, "Output",ExpressionUUID->"21b5cf8e-7f0a-45f7-ab93-9e8ebe789a07"]
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-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"],
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-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"],
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 }, Open  ]],
 Cell[CellGroupData[{
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-Cell[61523, 1473, 12321, 270, 180, "Output",ExpressionUUID->"2e45389f-59c7-4eaf-9b3a-270214fa013e"]
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 }, Open  ]],
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 Cell[CellGroupData[{
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-Cell[77594, 1862, 1944, 57, 77, "Output",ExpressionUUID->"0ca79efb-1867-4b1f-96fc-4a691d54b72e"]
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 Cell[CellGroupData[{
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 }, Open  ]],
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 Cell[CellGroupData[{
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-Cell[106252, 2506, 1298, 32, 44, "Output",ExpressionUUID->"6f1d902a-0431-4a99-adc2-97eb3c423317"]
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 }, Open  ]],
 Cell[CellGroupData[{
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-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"],
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 }
 ]
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)!