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BeginPackage["Schofield`"]
$Assumptions = {θc > 0, θc > 1, gC[_] ∈ Reals, B > 0, γ > 0}
β[D_:2] := Piecewise[
{
{1/8, D == 2},
{0.326419, D == 3},
{1/2, D == 4},
{β, True}
}
]
δ[D_:2] := Piecewise[
{
{15, D == 2},
{4.78984, D == 3},
{3, D == 4},
{δ, True}
}
]
α[D_:2] := Piecewise[
{
{0, D == 2},
{0.11008, D == 3},
{0, D == 4},
{α, True}
}
]
Δ[D_:2] := β[D] δ[D]
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]
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[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[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[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, m} ] /. θ -> 1
Φs = {
-1.197733383797993,
-0.318810124891,
0.110886196683,
0.01642689465,
-2.639978 10^-4,
-5.140526 10^-4,
2.08856 10^-4,
-4.4819 10^-5
}
Gls = {
0,
-1.3578383417066,
-0.048953289720,
0.038863932,
-0.068362119,
0.18388370,
-0.6591714,
2.937665,
-15.61
}
Ghs = {
0,
0,
-1.8452280782328,
0,
8.333711750,
0,
-95.16896,
0,
1457.62,
0,
-25891
}
dRule[sym_][f_, i_] := Derivative[i[[1]] - 1][sym][0] -> f (i[[1]] - 1)!
ΦRules = MapIndexed[dRule[Φ], Φs];
GlRules = MapIndexed[dRule[Gl], Gls];
GhRules = MapIndexed[dRule[Gh], Ghs];
rules[g_] := Join[{B -> ruleB[g]}, ΦRules, GlRules, GhRules]
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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