From 35f389dd892cffa997fbc67f9d1bc0aa2fb1564b Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Mon, 11 Dec 2023 18:07:04 +0100
Subject: Some changes.

---
 IsingScalingFunction.wl | 59 ++++++++++++++++++++++++++++++++++++++-----------
 1 file changed, 46 insertions(+), 13 deletions(-)

diff --git a/IsingScalingFunction.wl b/IsingScalingFunction.wl
index 81d5e47..92ed3e6 100644
--- a/IsingScalingFunction.wl
+++ b/IsingScalingFunction.wl
@@ -30,6 +30,8 @@ DScriptF0Dη::usage =
 
 DScriptMCasDξList::usage = "Computes the first m derivatives of the scaling function M given by Caselle et al."
 
+DScriptMCasDηList::usage = "Computes the first m derivatives of the scaling function M given by Caselle et al."
+
 uf::usage = "uf computes the singular free energy u_f."
 
 DufDut::usage =
@@ -46,6 +48,8 @@ Data::usage = "Data[n] gives data from the fit to nth order from Table II."
 
 PrepareArgument::usage = "Converts scaling function data into appropriate argument to function interfaces."
 
+DataCas::usage = "Data[n] gives data from the fit to nth order from Table II."
+
 θ0Cas::usage = "θ0 from Caselle et al."
 
 gsCas::usage = "g function coefficients from Caselle et al."
@@ -261,31 +265,60 @@ ruleB[θ0_, gs_] := (2 * OverlineS / π) * (- g[θ0, gs]'[θ0] / t[θ0]^Δ)
 
 ruleC0[θ0_, gs_] := Exp[Δ t[θ0]^(Δ - 1) t'[θ0] / (2 OverlineS / π g[θ0, gs]'[θ0]) - t[θ0]^Δ g[θ0, gs]''[θ0] / (4 OverlineS / π g[θ0, gs]'[θ0]^2)] t[θ0]^(1/8) OverlineS / (2 π) * g[θ0, gs]'[θ0]
 
-θ0Cas := Sqrt[1.16951];
+DataCas[2] = <|
+  "θ0" -> Sqrt[1.15278],
+  "gs" -> {1, -0.208408},
+  "ρ"  -> 2.01116
+|>
+
+DataCas[3] = <|
+  "θ0" -> Sqrt[1.15940],
+  "gs" -> {1, -0.215675, -0.039403},
+  "ρ"  -> 2.00770
+|>
+
+DataCas[4] = <|
+  "θ0" -> Sqrt[1.16441],
+  "gs" -> {1, -0.219388, -0.041791, -0.013488},
+  "ρ"  -> 2.00770
+|>
+
+DataCas[5] = <|
+  "θ0" -> Sqrt[1.16951],
+  "gs" -> {1, -0.222389, -0.043547, -0.014809, -0.007168},
+  "ρ"  -> 2.00881
+|>
 
-h0Cas := a b ρ /. {
+h0Cas[data_] := a b ρ /. {
     a -> c2^2/c4,
     b -> (-c4/c2^3)^(1/2),
-    ρ -> 2.00881
+    ρ -> data["ρ"]
   } /. {
     c2->Ghs[[3]] 2!,
     c4->Ghs[[5]]["Value"] 4!
   }
 
-gsCas := h0Cas * {
-    1,
-    -0.222389,
-    -0.043547,
-    -0.014809,
-    -0.007168
-  }
+gsCas[data_] := h0Cas[data] * data["gs"]
 
-m0Cas := -Ghs[[3]]2! h0Cas
+m0Cas[data_] := -Ghs[[3]]2! * h0Cas[data]
 
-DScriptMCasDξList[m_, θ_] := CompositeFunctionDerivativeList[
-    Identity, Function[θp, m0Cas * θp / RealAbs[θp^2 - 1]^β], ξ[θ0Cas, gsCas]
+DScriptMCasDξList[data_][m_, θ_] := CompositeFunctionDerivativeList[
+    Identity, Function[θp, m0Cas[data] * θp / RealAbs[θp^2 - 1]^β], ξ[data["θ0"], gsCas[data]]
   ][m, θ]
 
+DScriptMCasDηList[data_][m_] := With[{
+    FpmList = Table[(i - 1) / i, {i, 1, m + 1}] DScriptMCasDξList[data][m, θ]
+  },
+  Limit[
+  Table[D[η^2 * Fpm[η] - Log[η^2] / (8 π), {η, k}], {k, 0, m}] /.
+  {
+    η -> η[data["θ0"], gsCas[data]][θ],
+    Fpm[x_] :> Φs[[1]],
+    Derivative[i_][Fpm][x_] :> FpmList[[i]]
+  },
+  θ -> 1]
+  ]
+
 End[]
 
 EndPackage[]
-- 
cgit v1.2.3-70-g09d2