A Guide to Mathematical Tables. Supplement No. 1

199 Pages·1960·13.71 MB·English

by  N. M. Burunova, A. V. Lebedev and R. M. Fedorova (Auth.)

PUBLISHER'S NOTICE
TO REVIEWERS AND READERS
CONCERNING THE QUALITY OF PRODUCTION
AND PUBLISHED PRICE OF THIS WORK
We much regret that in the interest of speedily
making available the information contained in
this publication, it has been necessary to produce
the text by non-letterpress setting and photo
lithography, with the result that the quality of
production is not as high as the public have come
to associate with and expect from the Pergamon
Press.
To have re-set this manuscript by letterpress
would have delayed its appearance by many
months and the price would have had to be
increased further.
The cost of translating scientific and technical
works from the Russian in time, money, and
publishing effort is very considerable. In the
interest of getting the Soviet Authorities eventually
to pay the usual authors' royalties to Western
authors, the Pergamon Press is voluntarily paying
to Russian authors the usual authors' royalties
on this publication, in addition to the translators'
and editors' fees. This and the somewhat limited
market and the lack of any kind of subsidy
accounts for what may appear to be a higher
than usual published price.
I. R. MAXWELL
Publisher at Pergamon Press
A GUIDE TO
MATHEMATICAL TABLES
N. M. BURUNOVA
English edition prepared from the Russian by
D.G.FRY B.A. (Hons.)
Supplement No. 1
to
A Guide to
Mathematical Tables
by
A. V. Lebedev and R. M. Fedorovo
PERGAMON PRESS
OXFORD • LONDON • NEW YORK • PARIS
1960
PERGAMON PRESS LTD.,
Headington Hill Hall, Oxford.
4 and 5 Fitzroy Square, London W.l.
PERGAMON PRESS INC.,
122 East 55th Street, New York 22, NY.
1404 New York Avenue N.W., Washington 5, D.C.
P.O. Box 47715, Los Angeles, California.
PERGAMON PRESS S.A.R.L.
24 Rue des Ecoles, Paris Vc.
PERGAMON PRESS G.mb.H.
Kaiserstrasse 75, Frankfurt-am-Main.
Copyright
©
:960
Pergamon Press Ltd.
Library of Congress Card Number 60-10217
Printed in Great Britain by
PERGAMON PRINTING & ART SERVICES LTD.,
LONDON
TRANSLATOR'S PREFACE
Like the Guide, this Supplement has been
prepared from the original Russian edition by a
photographic process. The Russian text has been
replaced by English, but the tabular matter has
been reproduced direct from the original. The
necessary result of this is that Russian standard
notation is employed, which differs from that most
commonly employed in England as indicated in the
following table:
Russian English
tg tan
ctg cot -.
arc sin (etc) sin~x
lg log (base 10)
sh sinh
ch cosh
th tanh
cth coth T
ar sinh (etc) sinh""
-££ (-*) E (x) •
±
0°,1; 0,0001" (etc.) 0.1°; 0.0001"
Other comments on differences in presentation
made in the translator's preface to the Guide
apply with equal force to this Supplement.
A translation of titles given in Cyrillic
script in the reference section (Russian, Ukrainian
and Bulgarian), is to be found on pp.184 et seq.
Finally, the user of this Supplement is also
recommended to consult the translated preface to
the original Russian edition.
D. G. Fry.
This book is Supplement No. I to
A Guide to Mathematical Tables by
A.V. Lebedev and R.M. Fedorova,
also published by Pergamon Press
P R E F A CE
The present work is a continuation of the
Guide to Mathematical Tables compiled by
A.V. Lebedev and R.M. Pedorova and published by
the U.S.S.R. Academy of Sciences in 1956. It
contains information on tables which have been
published in the U.S.S.R. and abroad since the
publication of the Guide, and also on tables
which, for various reasons, did not find their
way into the Guide.
The holdings of the central libraries in the
U.S.S.R. have been used in the compilation of this
Supplement. Other sources include the abstracts
journal Mathematics up to 6, 1958, Mathematical
tables and other aids to computation up to 60,
1957 and Mathematical Reviews up~~t(r'8, 1958 (all
inclusive"}^
In a few cases the information given is not
complete as the reference was taken from one of the
journals mentioned above and not from the primary
source.
The material in this Supplement has been
arranged in the same way as in the Guide. The
chapter and section headings have been retained
with certain exceptions in which it has been
necessary to expand. Chapter 4 in the Guide,
for example, is entitled "Decimal and Natural
Logarithms'1, whereas in the Supplement it is
entitled "Logarithms" since logarithms with base
2 have been included. Where there is no new infor­
mation for a section in the Guide it is not
mentioned in the Supplement.
We have provided an index to the tables of
17 A Guide to Mathematical Tables
contents of both the Guide and the Supplement,
since these tables of contents are difficult to
use on account of their size. This index lists
all functions included in both the Guide and
the Supplement in the same order in which they are
encountered in the tables of contents, and the
pages on which they are to be found in both tables
of contents are given to the right. If, for
example, one wants information on existing tables
of Airy functions one establishes from the index
to the table of contents that Airy functions are
included in Chapter 10 and are listed on pages XXI
and XXIII in the tables of contents of the Guide
and the Supplement respectively.
The first part of the Supplement describes
mathematical tables in the following order:
1) the accuracy of the table, i.e. the number
of decimal places or significant figures;
2) the limits of variation of the argument
and the interval of the table;
3) the serial number of the book or journal
in the reference material in the second half of
the Supplement.
For example, the entry
4 dec. x = 0(0,1)3;>3 /15/
shows that the table gives values of the function
to four decimals for the argument x, which varies
from 0 to 3 in steps of 0.1 and for certain values
of x>3, and that this table is included in the
work mentioned under entry /15/ in the references
to the chapter concerned.
The following abbreviations have been adopted
in the descriptions of the tables:
exact - exact values
fig. or f. - significant figures.
Preface V
dec. or d. - decimal places
rec. - recurring decimal
(variable) or (var.) - variable step
h - hours
m - minutes (time)
sec. or s. - seconds (time)
g - grads (i.e. hundredths of a right angle)
c - hundredths of a grad
cc - ten thousandths of a grad
The Introduction to the Guide should be
consulted for other details concerning the descrip­
tion of tables and the symbols employed.
The second part of the Supplement contains a
list of the sources referred to in the first part.
The author, title, publishing house and date and
place of publication are given for books, and the
name of the journal, year of publication, series,
volume and number, page and author and title of
the article cited for journals.
If the book or journal is held in an open-
access library in Moscow or Leningrad, this library
is indicated after the title of the edition. When
a book has been issued in a large edition by a
Soviet publishing house a holding source has not
been indicated. (Translator's note. The information
referred to in this paragraph has been omitted from
the English edition).
The author wishes to express his deep gratitude
to K.A. Karpov for the attention which he has given
to the work and for valuable advice and assistance
during the preparation of the manuscript.
All comments and requests concerning the Guide
and the Supplement should be addressed to the
Computing Centre of the U.S.S.R. Academy of Sciences.
INDEX TO THE SECTION HEADINGS IN THE TABLE OF
CONTENTS OF THE GUIDE AND THE SUPPLEMENT
Guide Supp«
Chapter 1. Powers, rational and algebraic
functions • •• • • •• V X
Chapter 2. Trigonometric functions. Various
quantities connected with the circle
and the sphere • • • • • • • • • • • •• VII XI
Trigonometric and reciprocal
trigonometric functions VII XI
Quantities connected with the circle . IX XII
Quantities of the elements of a
triangle • • • • • • • • • • • • •• X
Areas and surfaces X XII
Volumes • • • • • • • • • • • • • •• X
Tables for conversion from the angular
measure to another X XII
Chapter 3* Exponential and hyperbolic
functions . . . . . ♦ . .♦ XI XIII
Chapter 4* Logarithms ♦ . XIII XIV
Common and natural logarithms and
antilogarithms of numbers and
trigonometric functions XIII XIV
Logarithms to base 2 - XIV
Chapter 5* Factorials, Euler integrals and
related functions • • • • • • • • • • •• XIV XV
Factorials XIV XV
The gamma function XIV XV
The psi function . XV XV
The beta function XV XVI
Chapter 6. Sine and cosine integrals,
exponential and logarithmic integrals and
related functions XVI XVI
Chapter 7. Probability integrals and related
functions XVII XVII
Probability distribution functions . ♦ XVII XVII
Probability integrals XVII XVII
Fresnel integrals and related
functions XXI XVIII
VIII Table of contents
Guide Supp.
Chapter 8. Elliptic integrals and elliptic
functions XXII XIX
Elliptic integrals and their moduli. XXII XIX
Jacobian and Weierstrassian elliptic
functions XXIV XX
Values of the Jacobian parameter XXIV XXI
The theta function XXIV XXI
Chapter 9* Polynomials and Legendre
functions XXV XXI
Chapter 10. Cylinder functions XXVI XXII
Cylinder functions of the first and
second kind of real argument • . • XXVI XXII
Riccati-Bessel functions XXVII XXII
Spherical Bessel or Stokes functions XXVIII
Lommel functions of two variables. . XXVIII XXII
Cylinder functions of the third kind
(Hankel functions) XXVIII XXII
Cylinder functions of the first and
second kinds of imaginary argument XXIX XXII
Thomson functions XXX XXIII
Airy functions XXXI XXIII
A special confluent hypergeometric
function - XXIV
Struve functions XXXI XXIV
Lommel-Weber functions XXXI
Zeros of cylinder functions • • • • XXXI XXIV
Integrals of cylinder functions . . XXXIII XXV
Chapter 11. Certain special functions and
integrals XXXIV XXVII
Chebyshev polynomials XXXIV XXVII
Chebyshev-Hermite polynomials . . . XXXIV XXVII
Jacobian polynomials XXXIV XXVII
Mittag-Leffler polynomials XXXIV
Laguerre polynomials . XXXIV XXVII
Neumann polynomials XXXV
Schlaffli's polynomials XXXV
Bernoulli polynomials . XXXV
Ruler polynomials XXXV
Various special polynomials . . .. XXXV XXVII
Biharmonic polynomials - XXVII
Riemann zeta function XXXV XXVII
Mathieu functions XXXV XXVII
Lame functions XXXVI
The hypergeometric function . . .. XXXVI XXVII