Elements of the Theory of Functions of a Complex Variable

Bücher

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Excerpt from Elements of the Theory of Functions of a Complex Variable: With Especial Reference to the Methods of Riemann Numerous additions have been made to Section IX., which treats of multiply connected surfaces. If Riemann's fundamental proposition on these surfaces be enunciated in such a form that merely simply connected pieces are formed by both modes of resolution, - as is ordinarily, and was also in § 49, the case, - then it must be supplemented for further applications. Such supplementary matter was given in § 52 in the classification of surfaces, and in § 53, V. But if we express the fundamental proposition in the form in which Riemann originally established it, in which merely simply connected pieces are formed by only one mode of resolution, while the pieces resulting from the other mode of resolution may or may not be simply connected, then all difficulties are obviated, and the conclusions follow immediately without requiring further expedients. This was shown in a supplementary note at the end of the book. 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.