add analytics

src/analytics.jl

@@ -69,3 +69,10 @@ function ϕ(T::Real, γ::Tuple{Real,Real})::Real
     return (a(T,γ)*T^2-b(T,γ)*T+c(T,γ))/log(γ[2]/γ[1])
 end
 
+function Λ(β::Tuple{Real,Real},γ::Real)::Real
+    a(β::Real,γ::Real)=(1-γ)*log((β+γ)/β)
+    b(β::Real,γ::Real)=γ*(gamma(0,β+γ)+(1-exp(-(β+γ)))/(β+γ))
+    c(β::Real,γ::Real)=exp(-γ)*expint(-β)-expint(-(β+γ))
+    return 1/γ^2*log(β[2]/β[1])*(a(β[2],γ)-a(β[1],γ)+b(β[2],γ)-b(β[1],γ)+c(β[2],γ)-c(β[1],γ))
+end
+