ON THE EVALUATION OF CERTAIN LATTICE SERIES

Abstract

Lattice series of the Madelung type are at best conditionally convergent; the values of such series, therefore, depend on the method of summation. A criterion is indicated for the choice of a method of summation leading to a physically significant value consistent with the problem in which such a series occurs. Evjen's method of grouping the terms of the series into particular units is discussed in detail for the CsCl type of lattice. It is found that in this case, his method fails to yield directly the unique physically significant value. An alternative method is proposed which leads at once to the unique value and is applicable to any series of the Madelung type.