From c9967adc9f7545667f747fd066ea61cbc20d8d13 Mon Sep 17 00:00:00 2001
From: Jaron Kent-Dobias <jaron@kent-dobias.com>
Date: Fri, 26 Mar 2021 17:17:45 +0100
Subject: Fixed efficiency problems, having convergence issues now.

---
 schofield.wl | 32 +++++++++++++++-----------------
 1 file changed, 15 insertions(+), 17 deletions(-)

(limited to 'schofield.wl')

diff --git a/schofield.wl b/schofield.wl
index 0d18848..646881d 100644
--- a/schofield.wl
+++ b/schofield.wl
@@ -35,28 +35,26 @@ t[θ_] := (θ)^2 - 1
 h[n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2i+1), {i, 0, n}]
 
 RFf[y_] := π^-1 y Exp[1/y] ExpIntegralEi[-1/y]
-RF[n_][θ_] := A (RFf[B(θc-θ)] + RFf[B(θc+θ)]) + Sum[FC[i] θ^(2i) , {i, 0, n}]
+RFnonsingular[n_][θ_] := A RFf[B(θc+θ)] + Sum[FC[i] θ^(2i) , {i, 0, n}]
+RF[n_][θ_] := A RFf[B(θc-θ)] + RFnonsingular[n][θ]
+
+RFfCoeff[m_] := 0 /; m < 2
+RFfCoeff[m_] := Gamma[m - 1] / π /; m > 1
 
 ruleB[g_] := π / (2 1.3578383417066) (- g'[θc] / t[θc]^Δ[2])
 
-eqLow[F_, h_][m_] := SeriesCoefficient[
-  F[θ] - t[θ]^2 (Gl[h[θ] t[θ]^-Δ[2]] + Log[t[θ]^2]/(8 π)),
-  {θ, θc, m},
-  Assumptions -> Join[$Assumptions, {θ < θc, θ > 1}]
-]
+eqLow[n_, h_][m_] := -A B^m RFfCoeff[m] + D[
+  RFnonsingular[n][θ] - t[θ]^2 (Gl[h[θ] t[θ]^-Δ[2]] + Log[t[θ]^2]/(8 π)),
+  {θ, m} ] / m! /. θ -> θc
 
-eqHigh[F_, h_][m_] := SeriesCoefficient[
-  F[θ] - (-t[θ])^2 (Gh[h[θ] (-t[θ])^-Δ[2]] + Log[(-t[θ])^2]/(8 π)),
-  {θ, 0, m},
-  Assumptions -> Join[$Assumptions, {θ > 0, θ < 1}]
-]
+eqHigh[n_, h_][m_] := D[
+  RF[n][θ] - (-t[θ])^2 (Gh[h[θ] (-t[θ])^-Δ[2]] + Log[(-t[θ])^2]/(8 π)),
+  {θ, m} ] /. θ -> 0
 
-eqMid[F_, h_][m_] := SeriesCoefficient[
-  F[θ] - t[θ]^2 Log[h[θ]^2]/(8 Δ[2]π) - h[θ]^((2-α[2])/Δ[2]) Φ[η]
+eqMid[n_, h_][m_] := D[
+  RF[n][θ] - t[θ]^2 Log[h[θ]^2]/(8 Δ[2]π) - h[θ]^((2-α[2])/Δ[2]) Φ[η]
     /. η -> t[θ] / h[θ]^(1 / Δ[2]),
-  {θ, 1, m},
-  Assumptions -> Join[$Assumptions, {θ > 0, θ < θc}]
-]
+  {θ, m} ] /. θ -> 1
 
 Φs = {
   -1.197733383797993,
@@ -103,7 +101,7 @@ GhRules = MapIndexed[dRule[Gh], Ghs];
 
 rules[g_] := Join[{B -> ruleB[g]}, ΦRules, GlRules, GhRules]
 
-eq[F_, g_][m_] := Select[Flatten[{eqLow[F, g][#], eqMid[F, g][#], eqHigh[F, g][#]} & /@ Range[0, m]] /. rules[g], !(# === 0) &]
+eq[F_, g_][m_] := Flatten[Join[{eqLow[F, g][#], eqMid[F, g][#]} & /@ Range[0, m], eqHigh[F, g] /@ Range[0, m, 2]]] /. rules[g]
 
 EndPackage[]
 
-- 
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