On a Certain Class of Functions Analogous to the Theta Functions (Classic Reprint)

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Excerpt from On a Certain Class of Functions Analogous to the Theta FunctionsMoreover, as M. Appell shows, these conditions are sufficient to determine q) (x, y, z) to within a constant factor.The object of the present paper is to investigate the properties of this function and of functions derived from it, as well as of others similar to it, pointing out, as far as possible, their analogy to those of the G-functions. As is not surprising, some of the properties of the latter seem to have no analogues in the case of the functions here considered. In such instances it has been endeavored to assign the reason, as far as possible.The great difficulty throughout the preparation of this thesis has been the utter poverty of known theorems holding for functions of more than one complex variable. As a consequence, this work has been rather of a tentative nature.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.