Ramanujan's Lost Notebook Part III
In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of
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George E. Andrews r Bruce C. Berndt
Ramanujan’s Lost Notebook Part III
George E. Andrews Department of Mathematics The Pennsylvania State University University Park, PA USA
Bruce C. Berndt Department of Mathematics University of Illinois at Urbana–Champaign Urbana, IL USA
ISBN 978-1-4614-3809-0 ISBN 978-1-4614-3810-6 (eBook) DOI 10.1007/978-1-4614-3810-6 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2005923547 Mathematics Subject Classification (2010): 11P82, 11P81, 11P84, 11P83, 33Dxx © Springer Science+Business Media New York 2012 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 publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
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I felt the joy of an explorer who suddenly discovers the key to the language lying hidden in the hieroglyphs which are beautiful in themselves. –Rabindranath Tagore, The Religion of Man
Preface
This is the third of five volumes that the authors plan to write in their examination of all the claims made by S. Ramanujan in The Lost Notebook and Other Unpublished Papers, which was published by Narosa in 1988. This publication contains the “Lost Notebook,” which was discovered by the first author in the spring of 1976 at the library of Trinity College, Cambridg
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