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]

f[θ_] := θ^2 - 1
g[gC_:gC, θc_:θc][n_][θ_] := (1 - (θ/θc)^2) Sum[gC[i] θ^(2i+1), {i, 0, n}]

I\[ScriptCapitalM]f[y_] := (1 + 1 / x) Exp[-1/x]
R\[ScriptCapitalM]f[y_] := (1 - y) Exp[1/y] ExpIntegralEi[-1/y] / (π y)

R\[ScriptCapitalM][2][B_, θc_, M0_][θ_] := - M0 (R\[ScriptCapitalM]f[B(θc - θ)] - R\[ScriptCapitalM]f[B(θc + θ)])

ruleB[2][f_, g_] := π / (2 1.3578383417066) (Δ g[θc] f[θc]^(-Δ[2]-1) f'[θc] - g'[θc] / f[θc]^Δ[2])

eqLow[D_:2][f_, g_][m_] := SeriesCoefficient[
  R\[ScriptCapitalM][D][B, θc, M0][θ] + f[θ]^β[D] Gl'[g[θ] / f[θ]^Δ[D]],
  {θ, θc, m},
  Assumptions -> Join[$Assumptions, {θ < θc, θ > 1}]
]

eqHigh[D_:2][f_, g_][m_] := SeriesCoefficient[
  R\[ScriptCapitalM][D][B, θc, M0][θ] + (-f[θ])^β[D] Gh'[g[θ] / (-f[θ])^Δ[D]],
  {θ, 0, m},
  Assumptions -> Join[$Assumptions, {θ > 0, θ < 1}]
]

eqMid[D_:2][f_, g_][m_] := SeriesCoefficient[
  R\[ScriptCapitalM][D][B, θc, M0][θ] + g[θ]^(1/δ[D]) ((2 - α[D]) Φ'[η] - η Φ'[η]) / Δ[D] /. η -> f[θ] / g[θ]^(1 / Δ[D]),
  {θ, 1, m},
  Assumptions -> Join[$Assumptions, {θ > 0, θ < θc}]
]

eq[D_:2][f_, g_][m_] := Flatten[{eqLow[D][f, g][#], eqMid[D][f, g][#], eqHigh[D][f, g][#]} & /@ Range[0, m]]

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[f_, g_] := Join[{B -> ruleB[2][f, g]}, ΦRules, GlRules, GhRules]

EndPackage[]