Ramanujan’s Notebooks
Part III
Bruce C. Berndt
Ramanujan’s Notebooks
Part III
Springer-Verlag
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Bruce C. Berndt
Department of Mathematics
University of Illinois at Urbana-Champaign
Urbana, IL 61801
USA
An earlier and shorter version of Chapter 16 was published in “Chapter 16 of Ramanujan’s second
notebook: Theta-functions and q-series,” by C. Adiga, B. C. Berndt, S. Bhargava and G. N.
Watson, Memoirs of the American Mathematical Society, Volume 53, Number 315, (January 1985).
The revised version in this book appears by permission of the American Mathematical Society.
AMS Subject Classifications: 10-00, lo-03,01A6O,OlA75, lOAxx, 33-xx
Library ofCongress Cataloging-in-Publication Data
(Revised for Part 3)
Ramanujan Aiyangar, Srinivasa, 1887-1920.
Ramanujan’s notebooks.
Includes bibliographical references and indexes.
1. Mathematics. I. Berndt, Bruce C., 1939-
11. Title.
QA3.R33 1985 510 84-20201
ISBN 0-387-96110-O (v. 1)
Printed on acid-free paper.
0 1991 Springer-Verlag New York Inc.
All rights reserved. This work may not be translated or copied in whole or in part without the
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The use of general descriptive names, trade names, trademarks, etc., in this publication, even if
the former are not especially identified, is not to be taken as a sign that such names, as understood
by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.
Typeset by Asco Trade Typesetting Ltd., Hong Kong.
Printed and bound by Edwards Brothers, Inc., Ann Arbor, MI
Printed in the United States of America.
987654321
ISBN o-387-97503-9 Springer-Verlag New York Berlin Heidelberg
ISBN 3-540-97503-9 Springer-Verlag Berlin Heidelberg New York
Dedicated to
S. Janaki Ammal
(Mrs. Ramanujan)
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