An expression for the sum of a series of terms which takes account of the different rates of oscillation of the functions involved is of importance for series such as occur in the problems of diffraction, and a relation of this kind has been given by Poisson. This relation can be written in the form
where Sm denotes the sum of m terms of the series Σun, beginning with the term un.
(Received December 12 1925)
(Accepted May 02 1925)