Formulas and Theorems for the Special Functions of Mathematical Physics
This is a new and enlarged English edition of the book which, under the title "Formeln und Satze fur die Speziellen Funktionen der mathe matischen Physik" appeared in German in 1946. Much of the material (part of it unpublished) did not appear in the ear
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H erau.fgegeben von
J. L. Doob
. E. Heinz· F. Hirzebruch . E. Hopf H. Hopf . W. Maak . S. Mac Lane W. Magnus· D. Mumford· F. K. Schmidt· K. Stein
(;eschaJftsJfuhrende lSlerausgeber
B. Eckmann und B. L. van der Waerden
Formulas and Theorems for the Special Functions of Mathematical Physics Dr. Wilhelm Magnus Professor at the New York University Courant Institute of Mathematical Sciences
Dr. Fritz Oberhettinger Professor at the Oregon State University Department of Mathematics
Dr. Raj Pal Soni Mathematician International Business Machines Corporation
Third enlarged Edition
Springer-Verlag Berlin Heidelberg GmbH 1966
Geschäftsfahrende Herausgeber :
Prof. DΓ. B. Eckmann Eidgenössische Technische Hochschule Zürich
Prof. Dr. B. L. van der Waerden Mathematisches Institut der Universität Zürich
ISBN 978-3-662-11763-7 ISBN 978-3-662-11761-3 (eBook) DOI 10.1007/978-3-662-11761-3 All rights reserved, especially that of translation into foreign languages. It is also forbidden to reproduce this book, either whole or in part, by photomechanical means (photostat, microfilm and/or microcard or any other means) without written permission from the Publishers © by Springer-Verlag Berlin Heidelberg 1966
Softcover reprint of the hardcover 1st edition 1966
Library of Congress Catalog Card Number 66-28437
Titel No. 5035
Preface This is a new and enlarged English edition of the book which, under the title "Formeln und Satze fur die Speziellen Funktionen der mathematischen Physik" appeared in German in 1946. Much of the material (part of it unpublished) did not appear in the earlier editions. We hope that these additions will be useful and yet not too numerous for the purpose of locating .with ease any particular result. Compared to the first two (German) editions a change has taken place as far as the list of references is concerned. They are generally restricted to books and monographs and accomodated at the end of each individual chapter. Occasional references to papers follow those results to which they apply. The authors felt a certain justification for this change. At the time of the appearance of the previous edition nearly twenty years ago much of the material was scattered over a number of single contributions. Since then most of it has been included in books and monographs with quite exhaustive bibliographies. For information about numerical tables the reader is referred to "Mathematics of Computation", a periodical published by the American Mathematical Society; "Handbook of Mathematical Functions" with formulas, graphs and mathematical tables National Bureau of Standards Applied Mathematics Series, 55, 1964, 1046 pp., Government Printing Office, Washington, D.C., and FLETCHER, MILLER, ROSENHEAD, Index of Mathematical Tables, Addison-Wesley, Reading, Mass.) .. There is a list of symbols and abbreviations at the end of the book. The formulas within each section are arranged in order of increasing complexity (a concept which, cannot of course, be sharply defined). We gratefully acknowledge the assistance of man
