Asymptotic Behavior of the t Expansion

The asymptotic behavior of a system's ground-state energy from the t expansion of Horn and Weinstein has been suggested to have the form E₁(t)=E₁+exp(–a_nt+b_n). In the limit of very large t, this becomes E₁(t)=E₁+exp(–a₁t+b₁). A simple analysis shows that the parameters are a₁=E₂–E₁ and b₁=ln[(E₂–E₁)|c₂|²/|c₁|²]. Functions are introduced which allow determination of a₁, b₁ and lower bounds to E₁.