Hypergeometric Summation An Algorithmic Approach to Summation and Sp
Modern algorithmic techniques for summation, most of which were introduced in the 1990s, are developed here and carefully implemented in the computer algebra system Maple™.The algorithms of Fasenmyer, Gosper, Zeilberger, Petkovšek and van Hoeij for hyperg
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Wolfram Koepf
Hypergeometric Summation An Algorithmic Approach to Summation and Special Function Identities Second Edition
Universitext
Universitext
Series editors Sheldon Axler San Francisco State University, San Francisco, CA, USA Vincenzo Capasso Università degli Studi di Milano, Milan, Italy Carles Casacuberta Universitat de Barcelona, Barcelona, Spain Angus MacIntyre Queen Mary University of London, London, UK Kenneth Ribet University of California, Berkeley, CA, USA Claude Sabbah CNRS, École Polytechnique Centre de mathématiques, Palaiseau, France Endre Süli University of Oxford, Oxford, UK Wojbor A. Woyczynski Case Western Reserve University, Cleveland, OH, USA
Universitext is a series of textbooks that presents material from a wide variety of mathematical disciplines at master’s level and beyond. The books, often well class-tested by their author, may have an informal, personal, even experimental approach to their subject matter. Some of the most successful and established books in the series have evolved through several editions, always following the evolution of teaching curricula, into very polished texts. Thus as research topics trickle down into graduate-level teaching, first textbooks written for new, cutting-edge courses may make their way into Universitext. For further volumes: http://www.springer.com/series/223
Wolfram Koepf
Hypergeometric Summation An Algorithmic Approach to Summation and Special Function Identities Second Edition
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Wolfram Koepf University of Kassel Kassel Germany
MapleTM is a trademark of Maplesoft, headquartered in Waterloo, Ontario, Canada (http://www. maplesoft.com/), and a member of Cybernet Systems Group, headquartered in Tokyo, Japan (http:// www.cybernet.co.jp/english/). The software of this book, as well as the MapleTM sessions, can be obtained from the book’s web site http://www.hypergeometric-summation.org.
ISSN 0172-5939 ISSN 2191-6675 (electronic) ISBN 978-1-4471-6463-0 ISBN 978-1-4471-6464-7 (eBook) DOI 10.1007/978-1-4471-6464-7 Springer London Heidelberg New York Dordrecht Library of Congress Control Number: 2014938224 Mathematics Subject Classification: 33C20, 33D15, 33F10, 68W30, 33C45, 33D45, 11B35, 05A19, 05A30, 11B65, 13P05 1st edition: Vieweg+Teubner Verlag, Wiesbaden, Germany 1998 Springer-Verlag London 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publi
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