数学函数手册HandbookofMathematicalFunctions_handbook

需积分: 50 33 浏览量更新于2023-03-16 评论 3 收藏 70.37MB PDF 举报

身份认证购VIP最低享 7 折!

领优惠券(最高得80元）

资源详情

资源评论

资源推荐

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 forpreliminarysurveys 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 of 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 particular 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 tbe 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.

ALLEN V. ASTIN, L?imctor.

Washington, D.C.

Preface to the Ninth Printing

The enthusiastic reception accorded the “Handbook of Mathematical

Functions” is little short of unprecedented in the long history of mathe-

matical tables that began when John Napier published his tables of loga-

rithms in 1614. Only four and one-half years after the first copy came

from the press in 1964, Myron Tribus, the Assistant Secretary of Com-

merce for Science and Technology, presented the 100,OOOth copy of the

Handbook to Lee A. DuBridge, then Science Advisor to the President.

Today, total distribution is approaching the 150,000 mark at a scarcely

diminished rate.

The success of the Handbook has not ended our interest in the subject.

On the contrary, we continue our close watch over the growing and chang-

ing world of computation and to discuss with outside experts and among

ourselves the various proposals for possible extension or supplementation

of the formulas, methods and tables that make up the Handbook.

In keeping with previous policy, a number of errors discovered since

the last printing have been corrected. Aside from this, the mathematical

tables and accompanying text are unaltered. However, some noteworthy

changes have been made in Chapter 2: Physical Constants and Conversion

Factors, pp. 6-8. The table on page 7 has been revised to give the values

of physical constants obtained in a recent reevaluation; and pages 6 and 8

have been modified to reflect changes in definition and nomenclature of

physical units and in the values adopted for the acceleration due to gravity

in the revised Potsdam system.

The record of continuing acceptance of the Handbook, the praise that

has come from all quarters, and the fact that it is one of the most-quoted

scientific publications in recent years are evidence that the hope expressed

by Dr. Astin in his Preface is being amply fulfilled.

LEWIS M. BRANSCOMB, Director

National Bureau of Standards

November 1970

Foreword

This volume is the result of the cooperative effort of many persons and a number

of organizations.

The National Bureau of Standards has long been turning out

mathematical tables and has had under consideration, for at least IO years, the

production of a compendium like the present one. During a Conference on Tables,

called by the NBS Applied Mathematics Division on May 15, 19.52, Dr. Abramo-

witz of t,hat Division mentioned preliminary plans for such an undertaking, but

indicated the need for technical advice and financial support.

The

Mathematics Division of the National Research Council has also had an

active interest in tables; since 1943 it has published the quarterly journal, “Mathe-

matical Tables and Aids to Computation” (MTAC),, editorial supervision being

exercised by a Committee of the Division.

Subsequent to the NBS Conference on Tables in 1952 the attention of the

National Science Foundation was drawn to the desirability of financing activity in

table production. With its support a z-day Conference on Tables was called at the

Massachusetts Institute of Technology on September 15-16, 1954, to discuss the

needs for tables of various kinds. Twenty-eight persons attended, representing

scientists and engineers using tables as well as table producers. This conference

reached consensus on several cpnclusions and recomlmendations, which were set

forth in tbe published Report of the Conference. There was general agreement,

for example, “that the advent of high-speed cornputting equipment changed the

task of table making but definitely did not remove the need for tables”. It was

also agreed that “an outstanding need is for a Handbook of Tables for the Occasional

Computer, with tables of usually encountered functions and a set of formulas and

tables for interpolation and other techniques useful to the occasional computer”.

The Report suggested that the NBS undertake the production of such a Handbook

and that the NSF contribute financial assistance. The Conference elected, from its

participants, the following Committee: P. M. Morse (Chairman), M. Abramowitz,

J. H. Curtiss, R. W. Hamming, D. H. Lehmer, C. B. Tompkins, J. W. Tukey, to

help implement these and other recommendations.

The Bureau of Standards undertook to produce the recommended tables and the

National Science Foundation made funds available.

To provide technical guidance

to the Mathematics Division of the Bureau, which carried out the work, and to pro-

vide the NSF with independent judgments on grants ffor the work, the Conference

Committee was reconstituted as the Committee on Revision of Mathematical

Tables of the Mathematics Division of the National Research Council.

This, after

some changes of membership, became the Committee which is signing this Foreword.

The present volume is evidence that Conferences can sometimes reach conclusions

and that their recommendations sometimes get acted on.

,/”

Handbook of Mathematical Functions

with

Formulas, Graphs, and Mathematical Tables

Edited by Milton Abramowitz and Irene A. Stegun

1. Introduction

The present Handbook has been designed to

provide scientific investigators with a compre-

hensive and self-contained summary of the mathe-

matical functions that arise in physical and engi-

neering problems. The well-known Tables of

Funct.ions by E. Jahnke and F. Emde has been

invaluable to workers in these fields in its many

editions’ during the past half-century. The

present volume ext,ends the work of these authors

by giving more extensive and more accurate

numerical tables, and by giving larger collections

of mathematical properties of the tabulated

functions. The number of functions covered has

also been increased.

The classification of functions and organization

of the chapters in this Handbook is similar to

that of An Index of Mathematical Tables by

A. Fletcher, J. C. P. Miller, and L. Rosenhead.

In general, the chapters contain numerical tables,

graphs, polynomial or rational approximations

for automatic computers, and statements of the

principal mathematical properties of the tabu-

lated functions, particularly those of computa-

tional importance. Many numerical examples

are given to illustrate the use of the tables and

also the computation of function values which lie

outside their range. At the end of the text in

each chapter there is a short bibliography giving

books and papers in which proofs of the mathe-

matical properties stated in the chapter may be

found. Also listed in the bibliographies are the

more important numerical tables. Comprehen-

sive lists of tables are given in the Index men-

tioned above, and current information on new

tables is to be found in the National Research

Council quarterly Mathematics of Computation

(formerly Mathematical Tables and Other Aids

to Computation).

The ma.thematical notations used in this Hand-

book are those commonly adopted in standard

texts, particularly Higher Transcendental Func-

tions, Volumes

1-3,

by A. ErdBlyi, W. Magnus,

F. Oberhettinger and F. G. Tricomi (McGraw-

Hill, 1953-55). Some alternative notations have

also been listed. The introduction of new symbols

has been kept to a minimum, and an effort has

been made to avoid the use of conflicting notation.

2. Accuracy of the Tables

The number of significant figures given in each

table has depended to some extent on the number

available in existing tabulations. There has been

no attempt to make it uniform throughout the

Handbook, which would have been a costly and

laborious undertaking. In most tables at least

five significant figures have been provided, and

the tabular’ intervals have generally been chosen

to ensure that linear interpolation will yield. four-

or five-figure accuracy, which suffices in most

physical applications. Users requiring higher

1 The most recent, the sixth, with F. Loesch added as cc-author, was

published in 1960 by McGraw-Hill, U.S.A., and Teubner, Germany.

2 The second edition, with L. J. Comrie added as co-author, was published

in two volumes in 1962 by Addison-Wesley, U.S.A., and Scientific Com-

puting Service Ltd., Great Britain.

precision in their interpolates may obtain them

by use of higher-order interpolation procedures,

described below.

In certain tables many-figured function values

are given at irregular intervals in the argument.

An example is provided by Table 9.4.

The pur-

pose of these tables is to furnish “key values” for

the checking of programs for automatic computers;

no question of interpolation arises.

The maximum end-figure error, or “tolerance”

in the tables in this Handbook is 6/& of

unit

everywhere in the case of the elementary func-

tions, and 1 unit in the case of the higher functions

except in a few cases where it has been permitted

to rise to

units.

IX /-

剩余1057页未读，继续阅读

一苇冯虚

粉丝: 8
资源: 11

会员权益专享

数学函数手册 Handbook of Mathematical Functions

评论0

会员权益专享

最新资源

数学函数手册 Handbook of Mathematical Functions

评论0

Handbook of Mathematical Functions

_Handbook.Of.Mathematical.Functions.

Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Table

handbook of mathematical models in computer vision, edited by nikos paragios

the mathematical-function computation handbook

详细谈谈你说的1,2两个近似

handbook of discrete and combinatorial mathematics

handbook of integral equations

master handbook of acoustics

the handbook of research synthesis and meta-analysis pdf

handbook of model checking

handbook of visual optics

handbook of mathematics

handbook of mathematics for engineers and engineering students pdf

handbook of chemistry and physics

handbook of linear partial differential equations

handbook of markov chain monte carlo

handbook of robotics中文版

handbook of hidden markov models in bioinformatics

handbook of natural language processing pdf

会员权益专享

最新资源