The complex functions of z, ⟨ α α z μ μ ( A ) B ⟩ converges in the complex strip − − β β < ℑ ℑ z < 0 whereas ⟨ B α α z μ μ ( A ) ⟩ converges in the complex strip 0 < ℑ ℑ z < β β if we make certain technical assumptions like the spectrum of H − μ N is bounded from below and its density does not increase exponentially (see Hagedorn temperature). If the functions converge, then they have to be analytic within the strip they are defined over as their derivatives,