with ν ν n = 2 π π n k B T / h , where k B and h are Boltzmann's and Planck's constants correspondingly. Inserting our relations for ρ ρ α α and approximating the sum as an integral k B T ∑ ∑ n = 0 , 1... ∞ ∞ → → h 2 π π ∫ ∫ ν ν 1 ∞ ∞ d ν ν , the effective Hamaker constant in the Lifshitz theory may be approximated as