Encyclopedia of mathematics and its applications – Baker G.A.
GIAN-CARLO ROTA, Editor ENCYCLOPEDIA OF MATHEMATICS AND ITS APPLICATIONS
Section: Mathematics of Physics Peter A. Carruthers, Section Editor
Los Alamos National Laboratory Los Alamos, New Mexico
University of Kent Canterbury, Kent, England
Los Alamos National Laboratory
Advanced Book Program Reading, Massachusetts
London 'Amsterdam - Don Mills, Ontario - Sydney - TokyoLibrary of Congress Cataloging in Publication Data
Baker, George A. (George Allen), Jr., 1932- Pade approximants.
(Encyclopedia of mathematics and its applications; 13- 14. Section, Mathematics of physics) Bibliography: p. Includes index.
Contents: pt. 1. Basic theory—pt. 2. Extensions and applications.
1. Padc approximant. I. Graves-Morris, P. R. (Peter Russell), 1941- II. Title. III. Series: Encyclopedia of mathematics and its applications; v. 13-14. IV. Series: Encyclopedia of mathematics and its applications. Section, Mathematics of physics. QC20.7.P3B35 530.1'514 81-3546 ISBN 0-201-13512-4 (v. 1) AACR2 ISBN 0-201-13513-2 (v. 2)
American Mathematical Society (MOS) Subject Classification Scheme (1980): 41A21
Copyright ©1981 by Addison-Wesley Publishing Company, Inc. Published simultaneously in Canada.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission of the publisher, Addison-Wesley Publishing Company, Inc., Advanced Book Program, Reading, Massachusetts 01867, U.S.A.
Manufactured in the United States of America
ABCDEFGHIJ-HA-8987654321To Our Wives Elizabeth Baker and Lucia Graves-Morris
and to Our Families
The poles and zeros of a high order Pade approximant of the exponential function delineate remarkable trajectories in the complex plane. The illustration, reproduced by kind permission of Professors E. B. Saff and R. S. Varga, conspicuously demonstrates the interplay and common features of many such trajectories. See pages 229 ff. for further details.Contents of Part I