The Messenger of Mathematics, Vol. 18

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Excerpt from The Messenger of Mathematics, Vol. 18: May 1888-April 1889The sixteen functions form one system. It is true that the Zeta functions are not doubly periodic, like the elliptic functions, but they are very nearly so, and, so to speak, they only just miss the property of complete double periodicity. An inspection of any of the systems of series for the sixteen functions shows not only that there exists a resemblance between the series representing the elliptic functions and those representing the Zeta functions, but that the latter are actually required in order to complete the four groups into which the former separate themselves. In fact, so perfectly alike in appearance are the representations of the elliptic and Zeta functions that it is always a curious and interesting matter to investigate, in the case of each system of series, the manner in which it is brought about that the Zeta series fail to attain the same amount of periodicity as that which is enjoyed by the others.This paper is not intended as a continuation of one which appeared with a nearly similar title* at the beginning of the last volume of the Messenger, but it may be regarded as forming a sequel to some portions of that paper.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.