O zastosowaniu sumowania według Eisensteina do pewnej sumy podwójnej

Abstract

The lattice sum $S_2$ for the square array conditionally converges. Having used physical arguments, Rayleigh chose an order of summation in such a way that $S_2$ = π. The Eisenstein summation method applied to $S_2$ yields the same result. This paper is devoted to a rigorous proof of $S_2$ = π for the Eisenstein summation method. The study can be used in class for students as an interesting example which illustrates different types of convergence.