Messenger of Mathematics, Vol. 11 (Classic Reprint)

Excerpt from Messenger of Mathematics, Vol. 11 Riemann, in a fragment published after his death in his collected works,* has determined the value of certain g series in the limiting case in which the analytical modulus of q is unity. If g=psi°, the series considered by Riemann contain 0 only, and converge and diverge for an infinite number of values of 9 between any two limits however near to one another; they appear, indeed, to have attracted Riemann's attention by this peculiarity. Two of these series, which may be regarded as examples of the rest, are considered in the present note, and some details relating to them are supplied which are omitted in Riemann's brief record of his results. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This 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.