BeginPackage["Schofield`"]

β::usage = "Gives the exponent for the magnetization."
δ::usage = "Exponent."
α::usage = "Exponent."
Δ::usage = "Exponent."

$Assumptions = {θc > 0, θi > 0, θc > θi, 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[θi_:1][n_][θ_] := (θ / θi)^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[γ_][y_] := (1 + (1 + γ x) / x) Exp[-1/x]
R\[ScriptCapitalM]f[γ_][y_] := (1 - y - γ y) Exp[1/y] ExpIntegralEi[-1/y] / (π y)

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

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