Encyclopedia of mathematics and its applications – Baker G.A.




Volume 13

Section: Mathematics of Physics Peter A. Carruthers, Section Editor

Padé Approximants

Part I: Basic Theory

 George A. Baker, Jr.

Los Alamos National Laboratory Los Alamos, New Mexico

Peter Graves-Morris

University of Kent Canterbury, Kent, England

 Foreword by Peter A. Carruthers

Los Alamos National Laboratory

Addison-Wesley Publishing Company

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