Complex Analysis
The idea of this book is to give an extensive description of the classical complex analysis, here ''classical'' means roughly that sheaf theoretical and cohomological methods are omitted. The first four chapters cover the essential core of complex analysi
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Complex Analysis Second Edition
ABC
Professor Dr. Eberhard Freitag
Dr. Rolf Busam
Universität Heidelberg Inst. Mathematik Im Neuenheimer Feld 288 69120 Heidelberg Germany [email protected]
Universität Heidelberg Inst. Mathematik Im Neuenheimer Feld 288 69120 Heidelberg Germany [email protected]
ISBN 978-3-540-93982-5
e-ISBN 978-3-540-93983-2
Library of Congress Control Number: 2008943985 Mathematics Subject Classification (2000): 30-01, 11-01, 11F11, 11F66, 11M45, 11N05, 30B50, 33E05 c 2009, 2005 Springer-Verlag Berlin Heidelberg ° This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg
Printed on acid-free paper 987654321 springer.com
In Memoriam Hans Maaß (1911–1992)
Meanwhile the fourth edition of the German version appeared. In this second English edition we adapt the content closely to this German edition. We also followed several suggestions and tried to improve the language and typography. We thank Shari Scott for her support.
Heidelberg, August 2008
Eberhard Freitag Rolf Busam
This book is a translation of the forthcoming fourth edition of our German book “Funktionentheorie I” (Springer 2005). The translation and the LATEX files have been produced by Dan Fulea. He also made a lot of suggestions for improvement which influenced the English version of the book. It is a pleasure for us to express to him our thanks. We also want to thank our colleagues Diarmuid Crowley, Winfried Kohnen and J¨ org Sixt for useful suggestions concerning the translation. Over the years, a great number of students, friends, and colleagues have contributed many suggestions and have helped to detect errors and to clear the text. The many new applications and exercises were completed in the last decade to also allow a partial parallel approach using computer algebra systems and graphic tools, which may have a fruitful, powerful impact especially in complex analysis. Last but not least, we are indebted to Clemens Heine (Springer, Heidelberg), who revived our translation project initially started by Springer, New York, and brought it to its final stage.
Heidelberg, Easter 2005
Eberhard Freitag Rolf Busam
Contents
I
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