TABLES OF INTEGRAL TRANSFORMS. Volume II. Based, in Part, on Notes Left by Harry Bateman Late Professor of Mathematics, Theoretical Physics, and Aeronautics at the California Institute of Technology.

468 Pages·1954·16.59 MB·English

by  Harry. A. Erdelyi (Editor of the Bateman Project. BATEMAN

CALIFORNIA INSTITUTE OF TECEVOTOGY
BATEMAN MANUSCRUPT PROJECT

A. Bendis, Eiitor
W. Macnuy, F Ossusnrtinenn, FG, Tarcome Research Assaeintes

Higher Transcondontal Functions, 3 volumes,
‘Tables of Integral ‘Transforms, 2 vouraes

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TABLES OF INTEGRA. TRANSFORMS

Volume I

Rawed, in put, un uvtes lett by

Harry Bateman

Lae Professor of Mathematics, Theoretical Physies, sud Aeronautics at
the California Institute of Techanlngy

saad eoupiled by the

Staff of the Baloman Yamuscript Project

Trapated at the Colifrnia Ireitute of Techuology xader Contract
TW, © Sonr-244 Tak Order XIV with the Qllfce of Navat Hescecch

Project Destgaation Noriher: VR 04-046

NEW YORK TORONTO LONDON
McGRAWIULL BOOK, COMPANY, INC.
1954
TARLES OF INTEGHAL TRANSEORMS. v0.11

COPYRIGHT, 1951, BY THE
MoGRAW.ATIL ROOK COMPAYY, INC.

PRINTED 1 1

ITED STAVES OF AMERICA

AU rights cevervnd meeap thoes guauted to the Thited Seater
Government. Otherwise, this lols or parta thera way not bo
produced ta. any foren without gormieian of tha pulshers,

1abvary of Congress Catalog Card Number: 31-6214

W550 v
Pe eee ere

pacer aU

o

This work is dediewed tw the
canary of

BARRY BATENAN

fas a ttibmte co the Imagination whict
lod him to undertnke 2 grojeer ot zis
siagnitude, and the scholarly

srhich inspire! hin: ww cary so far
toward completion.

j
:

STARF OF THE BATEMAN MANUSCIUPT PHOJECT

Direotur
Arthur Fadélyi

Research desoctates
Wilhelm Magnus (1918-50)

Brits Chorbortingor (148-51)
Fisueesay G, Triconi (1998-61)

Research Assistants
David Restin (1961-52)
WB, Falks (1949-50)

AWR, Tlarvey (1948-49)

DAL. Thomsen, Jr (1950-51)
Maria A, Reber (1849-51)
EuLs Whitaay (1948-49)

Varbaypies

Rosemarie Staupfet
aS a TEN ER EE SS ARETE EE OE
a

BReESTONEE

PREFACK,

‘The aima, the history, and the orgunization of these Fables of Tutegre?
Jrusaforms wore described in the Introduction ta vol. 1s A little more
‘han ove half of the present eeeond, and Jant, volure eousiate of tables
inf furthce inbegaut Lewforrs, the sen aining past of tiie value eontving
integrals of higher transcendental fonctions.

Tader [ne gouerie nant Fassel @onsforma we list not oaly the fowile
jar Huokel tranefonus Int alsy other transfonoation* whose kemcls ute
Benecl functions in the widest sense uf the word, a wldition to shese
se Tist fractional integrals, and also Stieltjes anc! Hithert transiunea. As
Jor us ore new, ao extensive tables oxist Jor any of the tanefareations
incluled in this voluve, in fact, for nome of Unet there are cunsparaively
for baown iaenform paires 4 Vist of ull wanslorms ineluded ia this work

ja given om pu xi

The cccond put of the volume contains misvellaneous integrols
jovalving higher sescendental fanetions, Sone af these integrals eannt
De onitten aa tranaforms, others sere nok included in the transform taliles
aad aro given here. Generally apeukingy om iatepral which eun be writen
faa a wanafonn i mote likely to be found ia the mransform tubles thus
auong iniesrale of higher Canscendentul funerionss The Jatner are a
unger aocording to their intexrands. The “ierareby”” of funclions given
doe paxdi of vole bias been followed andyies ia vole h composite functions
die cinacilici according to the “bigheat'® function ovcnering in there &
Vat of definitions of higher tunscendental fuuetious is given in the
Appendix

"Acksow ledgments and Usanke are due to the same persons and urgan=
izations a8 in conucetion with vul. I, Ackowlelgnents wre also duc tw
pw Joh Th Johmaton eho read the proofs andzeniezed other vsloahle

technical azsisLenee.
Comectinns of errors, additions, and suggestions for improvement wiTT
bbe sevcivel gratefully hy the Editors

A. FRDELY
erste enraennetnennagemamsernsy mint heuer
STANDARD FORMS

Fowriescosioe isansfona (f,, Chapeer
a2 FG) cos toy) dx

Fourier sine unsfovm (i, Chapter [)

14) ia fry) de

Exponential Fourier tsaneform (f, » Chapter 11)

SE Pore ae
Laplace tunsfor (8, Chapter 1¥)

JP fieye Mae

Inverse Laplace trunsiorm (Chaser ¥)

2ai

Mollin transfane (, Choyter VD
Jf" fled tt ae

4 Invesse Mallia tansform (Chapier V0)
2 L

q a

q Fat Aon

4 en hp
a IP Fadl fas ay as

8 ¥ straustoxm By Chapter IX)

‘| LF ¥en bar de
n