Closed-form evaluation of 2D static lattice sums
  In the present paper, employing properties of the complete elliptic integrals of the first and second kind, we deduce closed-form formulae for the lattice sums and other new formulae. Applications to the effective properties of regular and random composites are discussed. We also discuss the Eisenstein summation method and the Rayleigh method used in computations. 
Semyon Yakubovich, Piotr Drygas, Vladimir Mityushev
math.CA