Divergent Series, Summability and Resurgence II Simple and Multiple
Addressing the question how to “sum” a power series in one variable when it diverges, that is, how to attach to it analytic functions, the volume gives answers by presenting and comparing the various theories of k-summability and multisummability. These t
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Michèle Loday-Richaud
Divergent Series, Summability and Resurgence II Simple and Multiple Summability
Lecture Notes in Mathematics Editors-in-Chief: J.-M. Morel, Cachan B. Teissier, Paris Advisory Board: Camillo De Lellis, Zü rich Mario di Bernardo, Bristol Alessio Figalli, Austin Davar Khoshnevisan, Salt Lake City Ioannis Kontoyiannis, Athens Gabor Lugosi, Barcelona Mark Podolskij, Aarhus Sylvia Serfaty, Paris and New York Catharina Stroppel, Bonn Anna Wienhard, Heidelberg
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More information about this series at http://www.springer.com/series/304
Michèle Loday-Richaud
Divergent Series, Summability and Resurgence II Simple and Multiple Summability
Michèle Loday-Richaud LAREMA, Université d’Angers Angers, France
ISSN 0075-8434 ISSN 1617-9692 (electronic) Lecture Notes in Mathematics ISBN 978-3-319-29074-4 ISBN 978-3-319-29075-1 (eBook) DOI 10.1007/978-3-319-29075-1 Library of Congress Control Number: 2016940058 © Springer International Publishing Switzerland 2016 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. The use of general descriptive names, registered names, trademarks, service marks, 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
To Herv´e and Sylvie
Avant-Propos
Le sujet principal trait´e dans la s´erie de volumes Divergent Series, Summability and Resurgence est la th´eorie des d´eveloppements asymptotiques et des s´eries divergentes appliqu´ee aux e´ quations diff´erentielles ordinaires (EDO) et a` certaines e´ quations aux diff´erences dans le champ complexe. Les e´ quations diff´erentielles dans le champ complexe, et dans le cadre holomorphe, sont un sujet tr`es ancien. La th´eorie a e´ t´e tr`es active dans la deuxi`eme moiti´e du XIX-`eme si`ecle. En ce qui concerne les e´ quations lin´eaires, les math´ematiciens de cette e´ poque les ont subdivis´ees en deux classes. Pour la premi`ere, celle des e´ quations a` points singuliers r´eguliers (ou de Fuchs), g´en´eralisant les e´ quations hyperg´eom´etriques d’Euler et d
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