Exact results for some Madelung type constants in the finite-size scaling theory

A general formula is obtained from which the Madelung type constant: C(d|ν) = ∞ 0 dxx d/2−ν−1   ∞ l=−∞ e −xl 2 d − 1 − π x d 2   extensively used in the finite-size scaling theory is computed analytically for some particular cases of the parameters d and ν. By adjusting these parameters one can obtain different physical situations corresponding to different geometries and magnitudes of the interparticle interaction. In the analytic investigation of the finite-size scaling theory of systems undergoing phase transition the Madelung type constant [1]