The Handbook Of Mathematical Functions By Abramowitz And Stegun Pdf

UNITED STATES DEPARTMENT

OF

COMMERCE

•

Luther

H. Hodges

ecretary

NATIONAL

BUREAU OF STANDARDS

•

A

V

A.tiD,

Director

Handbook

of Mathematical Functions With

Formulas,

Graphs

and

Mathematical

Tables

Edited

by

Milton

AhraIIlowitz

and

Irene

A.

Stegun

National

Bureau

of

Standards

Applied Mathematics Series •

55

Issued

June

1964

Tenth

Printing,

December

1972

with corrections

For

ale

by

the

Superiotend

...

of Document..

U.S. Government

Printing Omce

W

ington.

D.C.

20402

-

Price

11.35

dOlDeetio

potItpaid,

or

flO.50

GPO

Book.tore

The

text

relating

to physical

constants

and

conversion

factors

page

6

has

been

modified

to

take

into

account

the

newly adopted

8ysteme

Interna-

tional d Unites

81).

ERR T

NOTICE

The

original

printing

of

this

Handbook

(June

1964

contained

errors

that

have been

corrected in

the

reprinted

editions.

These

cor

rections

are

marked with

an asterisk

*)

for

identification.

The

errors

occurred

on

the

following

pages:

2-3,6-8,10,15,19-20,25,76,85,91,102, 187, 189-197,218,223,225,233,250,255,260-263, 268,271-273,292,302, 328,332,333-337,362,365,415,423,438-440,443,445,447,449,451,484, 498,

505-506 509-510 543 556 558 562 571 5~5

599,600,722-723,

739, 742,

744 746 752 756 760-765 774 777-785 790 79~801 822-823 832

835,844, 886-889,897,914,915,

920 930-931~936 940-941 944-950 953

960, 963,

989-990, 1010,

1026.

Originally

issued

June

1964 . Second

printing,

November 1964.

Third

printing,

March

1965.

Fourth printing,

December 1965.

Fifth

printing

,

August

1966.

Sixth

printing,

November 1967 . Seventh

printing,

May 1968.

Eighth printing,

1969.

Ninth printing

, November 1970.

Librnry of Congress Catalog Card

Number:

64-60036

Preface

The

present volume is an outgrowth of a Conference on

Mathematical

Tables held

at

Cambridge Mass. on September 15-16 1954 under

the

auspices of

the

National Science Foundation

and

the

Massachusetts

Institute

of Technology.

The

purpose of

the

meeting was

to

evaluate

the

need for

mathematical

tables in

the

light of

the

availability of large scale computing machines.

It

was

the

consensus of opinion

that

in spite of

the

increasing use of

the

new machines

the

basic need for tables would continue

to

exist. Numerical tables of mathematical functions are in continual

demand

by

scien tists and engineers.

A

greater

variety

of functions

and

higher accuracy of

tabula-

tion are now required as a result of scientific advances and especially of

the

in creasing use of automatic computers.

In

the

latter

connection

the

tables serve mainly for preliminary surveys of problems before programming for machine operation.

For

those

without

easy access

to

machines such tables are of course indispensable. Consequently

the

Conference recognized

that

there was a pressing need for a modernized version of

the

classical tables of functions

I[ f

Jahnke-Emde.

To

imple

ment

the project

the National

Science

Foundation

requested

the

National

Bureau

of

Standards to

prepare such a volume

and

established

an Ad Hoc

Advisory Com mittee with Professor Philip M. Morse of

the

Massachusetts

Institute

of Technology as chairman

to

advise

the

staff of

the

National

Bureau

of

Standards

during

the

-course of

its

preparation.

In

addition

to the

Chairman

the Committee

consisted of

A.

Erdelyi M. C. Gray N. Metropolis

J.

B. Rosser

H.

C. Thacher

Jr. John

Todd C. B. Tompkins

and

J.

W. Tukey.

The primary

aim has been

to

include a maximum of useful information within

the

limits of a moderately large volume with particullar

attention to the

needs of scientists in all fields. An

attempt

has

been

made to

cover

the

entire field of special functions.

To

carry

out

the

goal

set

forth

by

the Ad

Hoc Committee

it

has

been necessary

to

supplement

the

tables

by

including

the mathematical

properties

that

are

important

in computation work as well as

by

providing numerical methods which demonstrate

the

use

and

extension of

the

tables.

The Handbook

was prepared under

the

direction

of

the late

Milton Abramowitz and Irene A. Stegun.

Its

success

has

depended greatly upon

the

cooperation of

many

mathematicians.

Their

efforts together with

the

cooperation of

the

Ad

Hoc

Committee are greatly appreciated.

The

particular

contributions of these

and other

individuals are acknowledged

at

appropriate places in

the

text.

The

sponsor ship of

the

National Science

Foundation

for

the

preparation of

the

material is gratefully recognized.

It

is hoped

that

this volume will

not

only meet

the

needs of all table users

but

will in

many

cases acquaint its users with new functions.

Ar.LEN

V.

ASTIN

Director

Washington D.C.

/

The Handbook Of Mathematical Functions By Abramowitz And Stegun Pdf

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