Lattice Green's Functions for the Cubic Lattices in Terms of the Complete Elliptic Integral

Abstract

The real and imaginary parts of the lattice Green's functions for the simple cubic (actually the tetragonal), body‐centered cubic, and face‐centered cubic lattices, at the variable from −∞ to +∞, are expressed as a sum of simple integrals of the complete elliptic integral of the first kind. The results of the numerical calculations obtained with the aid of the formulas are shown by graphs.