Tables of Integral Transforms - California Institute of Technology PDF
Preview Tables of Integral Transforms - California Institute of Technology
Tables of Integral Transforms CALIFORNIA INSTITUTE OF TECHNOLOGY BATEMAN MANUSCRIPT PROJECT A. ERDEL YI, Editor W. MAGNUS, F. 0BERHETTINGER, F. G. TRICOMI, Research Associates Higher Transcendental Functions, 3 volumes. Tables of Integral Transforms, 2 volumes. St7.7S"" BA V.2 Ceto- =L TABLES OF INTEGRAL TRANSFORMS Volume II A.rt. Based, in part, on notes left by Harry Bateman Late Professor of Mathematics, Theoretical Physics, and Aeronautics at the California Institute of Technology and compiled by the Staff of the Bateman Manuscript Project Prepared at the California Institute of Technology under Contract No. N 6onr-244 Task Order XIV with the Office of Naval Research Project Designation Number: NR 043-045 NEW YORK TORONTO LONDON McGRAW-HILL BOOK COMPANY, INC. 1954 TABLES OF lNTEGRAL TRANSFORMS, vol.IJ COPYRIGHT, 195,1, BY THE McGRAW-HILL ROOK COMPANY, INC. PRINTED IN THE UNITED STATES OF AMERICA All rights reserved except those granted to the United States GovPrnment. Otherwise, this book, or parts thereof, may not be rcprodueed in any form without pennission of the publishers. Library of Congress Catalog Card Number: 54-6214- 19550 9 10111213 141516-MAMM-7 6 54 This wNk is dedicated to the memory of HARRY B-ATEMAN as a tribute to the imagination which led him to undertake a project of this magnitude, and the scholarly dedication which inspired him to carry it so far toward completion. STAFF OF THE BATEMAN MANUSCRIPT PROJECT Director Arthur Erdelyi Research Associates Wilhelm Magnus (1948-50) Fritz Oberhettinger (1948- 51) Francesco G. Tricomi (1948-51) Research Assistants David Bertin ( 1951- 52) W.B. Fulks (1949-50) A.R. Harvey (1948- 49) D.L. Thomsen, Jr. (1950-51) Maria A. Weber (1949-51) E.L. Whitney (1948-49) V ari-typis t Rosemarie Stampfel PREFACE The aims, the history, and the organization of these Tables of Integral Transforms were described in the Introduction to vol. I. A little more than one half of the present second, and last, volume consists of tables of further integral transforms, the remaining_ part of this volume contains integriJ}S of higher transcendental functions. Under tl1e generic name Bessel trans forms we list not only the famil- iar Hankel transforms but also other transformations whose kernels are Bessel functions in the widest sense of the word. In addition to these we list fractional integrals, and also Stieltjes and Hilbert transforms. As far as we know, no extensive tables exist for any of the transformations included in this volume, in fact, for some of them there are comparatively few known transforrr. pairs. A list of all transforms included in this work is given on p. xi If. The second part of the volume contains miscellaneous integrals involving higher transcendental functions. Some of these integrals cannot be written as transforms, others Y\ere not included in the transform tables and are given here. Generally speaking, an integral which can be written as a transform is more likely to be found in the transform tables than among integrals of higher transcendental functions. The latter are ar- ranged according to their integrands. The "hierarchy" of functions given on p.xii of vol. I has been followed and, as in vol. I, composite functions are classified according to the "highest" function occurring in them. A list of definitions of higher transcendental functions is given in the Appendix. Acknowledgments and thanks are due to the same persons and organ- izations as in connection with vol. I. Acknowledgments are also due to Mr. John Q• Johnston who read the proofs and rendered other valuable technical assistance. Corrections of errors, additions, and suggestions for improvement will be received gratefully by the Editor. A, ERDELYI
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