Ten-Decimal Tables of the Logarithms of Complex Numbers and for the Transformation from Cartesian to Polar Coordinates 5707963268, 1415926536

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L.A. Lyusternik (Eds.) TEN-DECIMAL TABLES OF THE LOGARITHMS OF COMPLEX NUMBERS AND FOR THE TRANSFORMATION FROM CARTESIAN TO POLAR COORDINATES

TABLES OF THE FUNCTIONS

TEN-DECIMAL TABLES OF THE LOGARITHMS OF COMPLEX NUMBERS AND FOR THE TRANSFORMATION FROM CARTESIAN TO POLAR COORDINATES TABLES OF THE FUNCTIONS I n x , a r c t a n x , H n (1 + jc2), / \ + x 2 Edited by

L. A. LYUSTERNIK Translated by D. E. BROW N

PERGAMON PRESS O X F O R D • L ONDON • E D I N B U R G H ■ N E W Y O R K PARIS • FR A N K FU R T

1965

PE RGAMON P R E S S LTD. Heading ton Hill Hall, Oxford 4 & 5 Fitzroy Square, London W. 1 PERGAMON P R E S S (SCOTLAND) LTD. 2 & 3 Teviot Place, Edinburgh 1 PE RG AMO N P R E S S INC. 122 East 55th Street, New York 22, N.Y. G A U T H I E R - V I L L A R S ED. 55 Quai dee Grands-Augustine, Paris 6 PE RG AMO N P R E S S G.m.b.H. Kaiserstrasae 75, Frankfurt am Main Distributed in the Western Hemisphere by T H E MACMILLAN COMPANY • N E W YORK pursuant to a special arrangement with P erqam o n P r e s s L i m it e d

Copyright © 1965 P eroam o n P r e s s L t d .

Library of Congress Catalog Card Number 63-18926

This translation has been made from a book edited by L. A. Lyustemik entitled JlecRmuaHOHHbie madAUifbi Aoeapu&Moe KOMRAeiccHbix mice/i u nepexoda om fleicapmoeux Koopdunam k hoahphum. Ta6AUlfU 0yHKlfui In x, arctan x, J in (1 + x2) jAl+x2 (Tablitsy logarijmov kompleksnykh chisel i perekhoda ot Dekartovykh koordinat k polyamym. Tablitsy funlctsi* In x, arctan x, Jin (1+x2), j / l + x 2) published in 1952 by the Academy of Sciences of the U.S.S.R. Moscow

DESCRIPTION OF THE TABLES AND METHODS FOR THEIR USE T h e p r e s e n t tables were compiled in the Department for Approximate

Computations of the Institute of Exact Mechanics and Computational Methods of the U.S.S.R. Academy of Sciences. The computations were carried out by this department in conjunction with the ComputationalExperimental Laboratory of the Institute. The tables contain ten-decimal values of the following functions: 10, with interval 0.001

(a) In x

1

(b) i In (1 + x*)

0 s i < 1, with interval 0.001

(c) arctan x

O g i g 1, with interval 0.001

(d)

O f i i g 1, with interval 0.001

§ i
6460 3 38 6 4 5 1 784 6 4 4 5 223 6455

0 .5 8 0 0 .5 8 1 0 .5 8 2 0 .5 8 3 0 .5 8 4

6426 6418 6410 6401 6592

0 .5 8 5 0 .5 8 6

4 3 8 5 4 5 7 5555 4 * 8 9 0 0 6 3542

0 .5 3 4 5 1 6 5 8 1 1 7 4 0 1 6 1 7 6 4 9 2 0 5 3 5 2 5 6 5 4 2 8 7 3 '}') 124 6 4 9 2 0 .5 3 5 9 9 6 0 5 5 2 7 3 8 8 6 34 6 4 9 1

1 .1 6 1 0 7 7 0 8 62 1 .1 6 1 5 8 5 5 5 4 3 t . 1620946 603 1 .1 6 2 6 0 4 4 0 3 9 1 1631147837

0 .5 3 6 7 3 4 9 18 6 7 3 8 2 142 6 4 9 1 3 28 7375 655 6 4 9 0 981 7 3 6 9 1 6 3 6 4 9 0 144 7 3 6 2 6 7 3 6 4 8 9 8 1 7 7 5 5 6 186 6 4 8 8

i . 1636257 1 .1 6 4 1 3 7 4 x. 1646497 1 .1 6 5 1 6 2 6 1 .1 6 5 6 7 6 1

3468

o . 537475i 0 .5 3 8 2 1 0 6 0 .5 3 8 9 4 7 6 0 .5 3 9 6 8 3 8

102

0 .5 7 5

0 .5 7 8 0 .5 7 9

0 . 5 3 5 0 3 4 1 102 7 4 1 4 6 0 1 6 4 9 3 0 -5 3 5 7 7 5 5 705 7 4 0 8 108 6 4 9 2

3505 3491 3479

0 .5 7 1 0 .5 7 2

6511 6502 6494 6485 6477

4 5 7 8 321 5 5 8 i 4 ^ 8 1 8 0 6 5568

4399 577 4403 074 4406559 4410032

0 .5 6 0 0 .5 6 1 0 .5 6 2 0 .5 6 3 6 6 0 4 0 .5 6 4

1 . 1 5 3 0 2 9 0 5 4 3 4 9 8 1 4 5 2 6 5 1 9 0 -5 7 4

5594

4 3 9 6 0 6 5 3518

6 6 8 0 0-555 6 6 7 2 0 .5 5 6 6 6 6 3 0 -5 5 7 6 6 5 5 0 .5 5 8 6 6 4 6 0 -5 5 9 6657 6629 6620 6612

1 . 1 5 8 5 4 4 3 453 5 0 5 2 6 5 4 1 .1 5 9 0 4 9 6 10 7 5 0 5 9 0 7 6 1 .1 5 9 5 5 5 5 1 8 5 5 0 6 ; 4 9 0 1 .1 6 0 0 6 2 0 6 7 5 5071 8 9 6 1 . 1 6 0 5 6 9 2 5 6 9 5 0 7 8 295

4 3 9 2 543 3529

0 -555 0 .5 5 4

1 .1 4 6 1 2 3 9 0 2 6 4 8 8 9 553 1 .1 4 6 6 1 2 8 3 7 9 4 8 9 5 9 8 7 1 .1 4 7 1 0 2 4 3 6 6 4 9 0 2 6 1 2 1 .1 4 7 5 9 2 6 9 7 8 4 9 0 9 2 2 8 1 .1480836206 4915857

0 .5 2 9 3 1 7 0 6 9 7 7447 0 6 9 6494 0 .5 * 0 0 6 1 7 7 6 6 7 4 4 0 5 7 4 6494 0 .5 * 0 8 0 5 8 3 4 0 7 4 5 4 0 8 1 6 4 9 4 0 .5 3 1 5 4 9 2 421 7427 587 6 4 9 3 0 .5 3 2 2 9 2 0 0 0 8 7421 094 6493

5645 3652 5619 3607

0 .5 5 0 0 .5 5 1 0 .5 5 2

0 .5 7 5 0 .5 7 6

0 -5 7 7

0 .5 8 7 0 .5 8 8 0 .5 8 9

5 0 8 4 6 8 1 6 3 8 4 0 .5 9 0 5 0 9 1 0 6 2 6 5 7 6 0 .5 9 1 5 0 9 7 434 6 3 6 8 0 .5 9 2 5 1 0 5 7 98 ^ 5 5 9 0 .5 9 3 5 1 1 0 1 5 3 6 3 5 1 0 .5 9 4

990 5 1 1 6499 489 5122 839 328 5129 168 4 9 6 I5 I3 5 4 9 0 9 8 6 5 1 4 1 f io j

6 ) 4 3 0-595 6 3 5 4 0 .5 9 6 6 5 2 5 0 .5 9 7 6 3 1 8 0 .5 9 8 6 5 0 9 0 .5 9 9

X

j i n

( l + * a)

Ai

A2

o .f o o 0 .6 0 1 0 .6 0 2 0 .6 0 3 0 .6 0 4

0 .1 5 3 7 4 2 3 0 .1 5 4 1 8 3 6 0 .1 5 4 6 2 5 3 0 .1 5 5 0 6 7 4 0 .1 5 5 5 0 9 8

0 .6 0 5 0 .6 0 6 0 .6 0 7 0 .6 0 8 0 .6 0 9

0 .1 5 5 9 5 2 5 3 1 3 4 4 3 0 6 0 5 3 3 9 2 0 .1 5 6 3 9 5 5 9 1 8 4433 9 9 1 3379 0 .1 4 6 8 1 8 9 9 0 9 4 4 3 7 3 6 2 3 3 6 6 0 .1 5 7 2 8 2 7 271 4 4 4 0 723 3354 0 . 1 5 7 7 2 6 7 9 9 4 4 4 4 4 0 7 1 3341

0 .6 1 0 0 .6 1 1 0 .6 1 2 0 .6 1 3 0 .6 1 4

0 .1 5 8 1 7 1 2 0 6 5 0 .1 5 8 6 1 5 9 4 71 0 . 1 4 9 0 6 1 0 199 0 .1 4 9 4 0 6 4 2 1 8 0 .1 5 9 9 5 2 1 574

4 4 6 0 623 3280

0 .6 1 5 0 .6 1 6 0 .6 1 7 0 .6 1 8 0 .6 1 9

0 .1 6 0 3 9 8 2 0 .1 6 0 8 4 4 6 0 .1 6 1 2 9 1 3 0 .1 6 1 7 3 8 3 0 .1 6 2 1 8 5 7

197 093 250 655 298

4 4 6 7 1 5 7 33 54 4 4 7 0 4 0 5 3243 4473 643 3231 4476 866 3218

0 .6 2 0 0 .6 2 1 0 .6 2 2 0 .6 2 3 0 .6 2 4

0 .1 6 2 6 3 3 4 0 .1 6 3 0 8 1 4 0 .1 6 3 5 2 9 7 0 .1 6 3 9 7 8 3 0 .1 6 4 4 2 7 3

164 243 520 986 628

4480 4483 4486 4489 4492

0 .6 2 5 0 .6 2 6 0 .6 2 7 0 .6 2 8 0 .6 2 9

0 .1 6 4 8 7 6 6 0 .1 6 5 3 2 6 2 0 .1 6 5 7 7 6 1 0 .1 6 6 2 2 6 3 0 .1 6 6 6 7 6 9

432 187 482 704 040

4 4 9 5 955 3 1 4 6 4 4 9 9 0 95 3134

4 9 8 4 4 1 3 494 3454 9 9 2 4 4 1 6 9 4 0 3441 9 3 2 4 4 2 0 3 7 5 3439 307 4433 798 3416 105 4 4 2 7 2 0 8 3403

0 .6 3 0 0 .6 3 1 0 .6 3 2 0 .6 3 3

0 .1 6 7 1 2 7 7 4 7 9 0 .1 6 7 5 7 8 9 0 0 9 0 .1 6 8 0 3 0 3 6 1 7 0 .1 6 8 4 8 2 1 2 9 2 0 .6 3 4 0 . 1 6 8 9 3 4 2 0 2 2

0 .6 3 5 0 .6 3 6 0 .6 3 7 0 .6 3 8 0 .6 3 9

4447 4o6 3328 4 4 5 0 728 33*7 4454059 3304 4 4 5 7 336 3 2 9 2

4463 896 5267

079 277 406 642 804

3206

5193 3182 3169

3*57

4 5 0 2 22 2 ^121 4505 356 3109 4 5 0 8 439 3°97 4511 530 4514 608 4517675 4520 730

3084

3073 3061

3049 4 5 2 3 773 3 036

0 .1 6 9 3 8 6 5 795 4 5 2 6 8 0 3 30 2 5 0 . 1 6 9 8 3 9 2 5 9 8 4 5 2 9 8 2 2 30 1 3 0 .1 7 0 2 9 2 2 4 20 4 5 3 2 8 2 9 3001 0 . 1 70 7 4 5 5 2 4 9 4 5 3 5 8 2 4 2 9 9 0 0 .1 7 1 1 9 9 1 0 7 3 4 5 3 8 8 0 8 2 9 7 7 0 .1 7 1 6 5 2 9 0 .1 7 2 1 0 7 1 0 .1 7 2 5 6 1 6 0 .1 7 3 0 1 6 4

881 660 398 085

4541 779 4 5 4 4 738 4547687 4 5 5 0 621

0 .6 4 5 0 . 1 7 3 9 2 6 8 0 .6 4 6 0 . 1 7 4 3 8 2 4 0 .6 4 7 0 . 1 7 4 8 3 8 4 0 .6 4 8 0 . 1 7 5 2 9 4 6 0 .6 4 9 0 .1 7 5 7 5 1 1

251 711 070 318

4 5 5 6 4 5 8 2906 2895 2884 2872 2859

0 .6 4 0 0 .6 4 1 0 .6 4 2 0 .6 4 3 0 .6 4 4

2965

2954

2942 2950 0 - l 7347I 4 706 4553 547 2 9 I9

4559359 4562 248 4565126 444 4 5 6 7 9 9 2

a rc tg x

- A 2

V 1+xs

A,

a

2

X

1 .1 6 6 1 9 0 3 7 9 0 5 1 4 8 1 0 8 6 3 0 1 o .6 c o

6488 6487 6487 6486 0 - 5 4 3 3 5 5 4 S 7 1 7 3 3 3 753 6 4 8 5

1 .1 6 7 2 2 0 6 30 4 5 1 6 0 6 9 4 6 2 8 4 o .6 o r 1 . 1 6 7 7 3 6 6 9 9 8 5 1 6 6 9 7 4 6 2 7 5 0 .6 0 3 1 . 1 . 6 8 2 5 3 3 9 7 2 5 1 7 5 2 4 5 6 2 6 8 0 .6 0 4

0 .5 4 4 0 8 7 8 6 2 4 0 .5 4 4 8 1 9 5 8 9 2 0 .5 4 5 5 5 0 6 6 7 7 0 .5 4 6 2 8 1 0 9 7 9 0 .5 4 7 0 1 0 8 7 98

6484 6483 6483 6482 6480

1 .1 6 8 7 7 0 7 2 1 7 1 .1 6 9 2 8 8 6 7 2 7 1 .1 6 9 8 0 7 2 4 91 1 .1 7 0 3 2 6 4 5 0 2 1 .1 7 0 8 4 6 2 751

5179510 5185 764 3192 011 5198 249 5204 480

6 2 5 9 0 .6 0 5 6 2 5 0 0 .6 0 6 6 2 4 2 0 .6 0 7 6 2 3 4 0 .6 0 8 6 2 2 6 0 .6 0 9

6480

1 .1 7 1 3 6 6 7 2 31 1 .1 7 1 8 8 7 7 9 3 3 1 .1 7 2 4 0 9 4 8 4 8 1 .1 7 2 9 3 1 7 9 6 8 1 .1 7 3 4 5 4 7 2 8 6

5210 5216 5223 5229 5235

702 915 120 318 506

6217 6209 6201 6195 6184

0 .6 1 0 0 .6 1 1 0 .6 1 2 0 .6 1 3 0 .6 1 4

1 .1 7 3 9 7 8 2 79 2 5241 6 8 6 1 .1 7 4 5 0 2 4 4 7 8 5 2 4 7 8 5 9 1 .1 7 5 0 2 7 2 3 3 7 5 2 5 4 0 2 3 1■ i 75553 6 360 S 260 178 1 .1 7 6 0 7 8 6 5 3 8 5 2 6 6 32 6

6176 6168 6160 6153 6144

0 .6 1 5 0 .6 1 6 0 .6 1 7 0 .6 1 8 0 .6 1 9

1 .1 7 6 6 0 5 2 8 6 4 5 2 7 2 46 5 6 1 5 5 1■i 7 7 l 32 5 33 9 5 2 7 8 596 6 1 2 6 1 .1 7 7 6 6 0 3 9 25 5 2 8 4 7 1 8 6 t 18 1 .1 7 8 1 8 8 8 6 43 5 2 5 0 8 3 3 6 1 1 0 i . i 7 8 7 I 79 476 5 2 9 6 9 5 9 6 1 0 2

0 .6 2 0 0 .6 2 1 0 .6 2 2 0 .6 2 3 0 .6 2 4

1 .1 7 9 2 4 7 6 4 1 5 5303 0 3 7 1 .1 7 9 7 7 7 9 4 5 2 5 3 0 9 1 2 7 1 .1 8 0 3 0 8 8 5 7 0 5 3 1 5 2 0 8 1 .1 8 0 8 4 0 3 7 8 7 5 3 2 1 2 8 2 i . 1 .8 1 3 7 2 5 0 6 9 5 3 2 7 3 4 6

0 .0 2 ^ 0 .6 2 6 0 .6 2 7 0 .6 2 8 0 629

0 . 5 4 0 4 1 9 5 C05 7 3 4 9 6 9 7 0 .5 4 1 1 5 4 4 7 0 0 7343 2 1 0 0 .5 4 1 8 8 8 7 9 1 0 7 3 3 6 7 2 4 0 .5 4 2 6 2 2 4 6 3 4 7330 237

7317268 7 5 1 0 785 7304 302 7297 819 7291 339

0 .5 4 7 7 4 0 0 1 3 7 7284 859 0 . 5 4 8 4 6 8 4 9 9 6 7 2 7 8 3 79 0 . 5 4 9 1 9 6 5 575 7 2 7 1 9 0 1 0 .5 4 9 9 2 3 5 2 7 6 7 2 6 5 4 2 4 0 .5 5 0 6 5 0 0 7 0 0 7 2 5 8 9 4 7

0 .5 5 1 3 7 5 9 6 4 7 7252 472 0 .5 5 2 1 0 1 2 119 724 5 9 9 7 0 . 5 5 2 8 2 5 8 n 6 73 3 9 5 3 4 0 .5 5 3 5 4 9 7 640 7 2 3 3 0 5 2 0 .5 5 4 2 7 3 0 6 9 2 7 2 2 6 581

6479 6478

6477 6476

6475 6474 6473 6472 6470

0 . 5 5 4 9 9 5 7 2 7 3 7 2 2 0 T1 1 6 4 6 9 0 .5 5 5 7 1 7 7 3 8 4 7 2 1 3 6 4 3 6 4 6 8 0 .5 5 6 4 3 9 1 0 2 7 7 2 0 7 175 6 4 6 7 0 .5 5 7 1 5 9 8 2 0 2 7 2 0 0 708 6 4 6 6 0 .5 5 7 8 7 9 8 9 1 0 7 1 9 3 2 4 3 6 4 6 4

0 . 5 5 8 5 9 9 3 i 53 7 1 8 7 7 8 0 6 4 6 3 0 .5 5 9 3 1 8 0 9 3 5 0 .5 6 0 0 3 6 2 2 5 0 0 .5 6 0 7 5 3 7 106 0 .5 6 1 4 7 0 5 5 0 2

7 1 8 ' 317 6462 7174 856 6461 7168 iq 6 6460 7161 937 6458

0 .5 6 2 1 8 6 7 44q 0 .5 6 2 9 0 2 2 9 1 9 0 .5 6 3 6 1 7 1 944 0 .5 6 4 3 3 1 4 5 14 0 .5 6 5 0 4 3 0 6 3 1

7155 480 7149 025 7142570 7136 117 7129 666

6456 6455 6454 6452 6450

0 . 5 6 5 7 5 8 0 2 Q7 7 1 2 3 2 1 7 6 4 4 9 0 .5 6 6 4 7 0 3 31 4 0 .3 6 7 1 8 2 0 2 8 2 0 .3 6 7 8 9 ^ 0 601 0 .5 6 8 6 0 3 4 4 7 9

7116 768 6448 71 t o 3 2 1 6 4 4 6 7 103 876 6444 7 0 9 7 4 33 6 4 4 3

] . 1 6 6 7 0 5 1 8 9 8 5 1 5 4 4 0 6 6 2 9 3 0 .6 0 1

6004 6086 6078 6069 6061

1 .1 8 1 5 0 5 2 1 .1 8 2 4 3 8 5 1 .1 8 2 9 7 2 5 1 .1 8 3 5 0 7 0 1 .1 8 4 0 4 2 2

415 819 272 764 250

5 5 5 7 549 6 0 : 0 0 .6 3 4

1 .1 8 4 5 7 7 9 1 .1 8 5 1 1 4 3 1 .1 8 5 6 5 1 2 1 .1 8 6 1 8 8 8 1 .1 8 6 7 2 7 0

839 405 978 551 116

5 3 0 3 5 6 6 6 0 1 2 0 .6 3 5 5 3 69 571 6 0 0 4 0 . 6 3 6 5375 573 5 9 9 6 0 . 6 3 7 5 3 8 1 5 6 5 598 7 0 .6 3 8 5 5 8 7 5 4 8 5979 0 .6 3 9

5333 404 6 0 5 3 0 .6 3 0 5 3 3 9 4 53 6 0 4 4 0 .6 3 1 5345 4 9 2 6 0 3 6 0 .6 3 2 5 3 5 1 5 2 6 6 0 2 8 0 .6 3 3

0 .5 6 9 3 1 3 1 q i t 7090 990 6441 0 . 5 7 0 0 2 2 a 9 0 1 7 0 8 4 3 51 6 4 4 0 0 .5 7 0 7 3 0 7 4 5 2 7078 i n 6459 0 .5 7 1 4 3 8 5 565 7 0 7 1 6 7 4 6 4 3 6 O .5 7 2 1 4 5 7 2 3 7 7 0 6 5 2 4 0 6435

1 .1 8 7 2 6 5 7 6 6 4 1 .1 8 7 8 0 5 i 187 1 .1 8 8 3 4 5 0 6 7 7 1 .1 8 8 8 8 5 6 127 1 .1 8 9 4 2 6 7 52 7

5393 5 2 3 5 9 7 i 539 9 4 9 0 5963 5 4 0 5 4 5 0 5955 5411 4 0 0 5647

O .5 7 2 8 5 2 2 4 7 7 7 0 5 8 0 - 573558i 282 7052 O .5 7 4 2 6 5 3 6 5 6 7 0 4 5 0 . 5 7 4 9 6 7 9 601 7039 0 .5 7 5 6 7 1 9 116 7 0 3 3

1 .1 8 9 9 6 8 4 1 .1 9 0 5 1 0 8 1 .1 9 1 0 5 3 7 1 .1 9 1 5 9 7 2 I . 1021413

5 4 2 3 2 7 7 5 9 3 ° 0 .6 4 5 5 4 2 9 2 0 4 5925 0 .6 4 6

103

805 6453 374 6 4 3 0

945 6 4 3 0 515 6 4 2 7 09 0 6425

870 147 351 474 5O7

0 .6 4 0 0 .6 4 1 0 .6 4 2 0 .6 4 3 5 4 x7 343 5 9 3 8 0 .6 4 4

5435 1 2 3 5 9 1 4 0 . 6 4 7 5 4 4 i 0 3 3 5906 0 .6 4 8 5 4 4 6 9 3 5 5 8 9 8 0 .6 4 9

X

1 — \ n ( 1 + J f a)

A!

a

2

a r c lg x

A,

— A,

V l + x

A, 1

0.650 0 . 1 7 6 2 0 7 9 0.651 o . 1 7 6 6 6 5 0 0.652 o . 1 7 7 1 2 2 3 0.653 o . 1 7 7 5 8 0 0 0.654 0 . 1 7 8 0 3 7 9

4 3 6 4570844 280 4573 688 968 4 5 7 6 5 1 8 486 4 5 7 9 3 3 7 823 4 5 82 * 4 5

2848 2837 2825 2814 2802

0 .5 7 6 3 7 5 2 2 0 6 7 0 2 6 665 0 .5 7 7 0 7 7 8 871 7 0 2 0 2 4 2 0 - 5 7 7 7 7 9 9 ” 3 7013 822 0 .5 7 8 4 8 1 2 9 3 5 7 0 0 7 4 03 0 .5 7 9 1 8 2 0 338 7 0 0 0 9 8 6

6424 6422 6420 6418 6416

5452 829 5 8 9 O O.65O 5458 715 5 8 8 2 O.65I 1.1937771 986 5 4 6 4 5 9 4 5 8 7 4 O.652 I . 1 9 4 3 2 3 6 5 80 5470 463 5 8 6 5 O.653 I . I9 4 8 7 O 7 0 4 3 5476 325 5 8 5 8 O.654

6414 6412 6410 6408 6406

I . I 9 5 4 1 8 3 368 179 5 8 5 O 1 .1 9 5 9 6 6 5 547 5 4 8 8 0 2 5 5842 I . I 9 6 5 1 5 3 5 7 2 5 4 9 3 862 5 8 3 4 I.I970647434 5 4 9 9 8 9 3 5 8 2 6 1 . 1 9 7 6 1 4 7 127 5 5 0 5 5 M 5818

O.655 O.656 O.657 O.658 O.659

1 .1 9 8 1 6 5 2 1 .1 9 8 7 1 6 3 I .1 9 9 2 6 8 1 1 .1 9 9 8 2 0 4 1 .2 0 0 3 7 3 2

641 5 511 327 5 810 968 5 5 i 7 » 3 3 5802 >01 5 5 2 2 9 3 1 5 7 9 4 0 3 2 552 8 721 5 7 8 5 753 5 5 3 4 502 5 7 7 7

0 .6 6 0 0 .6 6 1 0 .6 6 2 0 .6 6 3 0 .6 6 4

1 .2 0 0 9 2 6 7 255 5 5 4 0 2 7 6 5 7 6 9 1 .2 0 1 4 8 0 7 5 3 1 5 5 4 6 0 4 1 5761 1 .2 0 2 0 3 5 5 5 7 2 5 5 5 1 7 9 9 5 7 5 4 1 .2 0 2 5 9 0 5 3 7 1 5 5 5 7 5 4 9 5 7 4 8 1 .2 0 3 1 4 6 2 9 2 0 5 5 6 3 2 9 1 5 7 3 7

0 .6 6 5 0 .6 6 6 0 .6 6 7 0 .6 6 8 0 .6 6 9

1 .2 0 3 2 0 2 6 2 1 1 1 .2 0 4 2 5 9 5 235 1 .2 0 4 8 1 6 9 9 8 6 1 .2 0 5 3 7 5 0 4 5 4 1 .2 0 5 9 3 3 6 6 3 2

575° i 5722 5580 468 5 7 * 4 5 5 8 6 1 7 8 5706 5591 880 5698

0 .6 7 0 0 .6 7 1 0 .6 7 2 0 .6 7 3 0 .6 7 4

1 .2 0 6 4 9 2 8 5 1 2 1 .2 0 7 0 5 2 6 0 8 6 1 .2 0 7 6 1 2 9 3 4 7 1 .2 0 8 1 7 3 8 2 8 6 1 .2 0 8 7 5 5 2 8 9 5

5603 261 5608939 5614 609 5620271

4 5 8 4 9 4 i 2790 4587725 2 7 7 9 4590 498 2768 4 5 9 3 2 6 0 2756 4596 010 2 7 4 4

0 .5 7 9 8 8 2 1 32 4 0 .5 8 0 5 8 1 5 895 0 .5 8 1 2 8 0 4 0 5 3 0 .5 8 1 9 7 8 5 8 0 0 0 .5 8 2 6 7 6 1 1 3 9

6994571 69 8 8 158 6981 747 6975 339 6968 931

0.660 o . 1 8 0 7 9 1 4 4 0 2 4 5 9 8 7 4 8 2 7 3 3

0 .5 8 3 3 7 3 0 0 7 0 0 .5 8 4 0 6 9 2 596 0 .5 8 4 7 6 4 8 7 2 0 0 .5 8 5 4 5 9 8 4 4 3 0 .5 8 6 1 5 4 1 7 6 8

6962 6956 6949 6943 6936

0 .6 5 5 0 .6 5 6 0 .6 5 7 0 .6 5 8 0 .6 5 9

o. o. o. o. o.

1784961 968 1789546 9°9 1794134634 1 7 9 8 7 2 ;, 1 3 2 18 0 3 3 1 8 392

0.66l

4601475 4 6 0 4 191 4606 896 4609 588

2722 2711 2698 2687

>.665 o . 1 8 3 0 9 3 5 3 0 0 4 6 1 2 2 7 0 4614 9 4 ° >.667 0 . 1 8 4 0 1 6 2 5 1 0 4 6 1 7 5 9 9 1.668 o . 1 8 4 4 7 8 0 1 0 9 4 6 2 0 2 4 7 1.669 o . 1 8 4 9 4 0 0 3 5 6 4 6 2 2 8 8 3

2676 2665

O .1 8 1 2 5 1 3 1 5 ° 0.662 o . 1 8 1 7 1 1 4 6 2 5 O.663 o . 1 8 2 1 7 1 8 8 1 6 1.664 o . 1 8 2 6 3 2 5 7 1 2

).666 0 . 1 8 3 5 5 4 7 5 7 °

2654 2642 2631

2619 2608 2597 2586

0 .1 8 5 4 0 2 3 2 39 4 6 2 5 0 .1 8 5 8 6 4 8 7 4 8 4 6 2 8 0 .1 8 6 3 2 7 6 8 7 0 4 6 3 0 0 .1 8 6 7 9 0 7 5 9 5 4 6 3 3 3 .6 7 4 0 . 1 8 7 2 5 4 0 9 1 1 4 6 3 5

509 122 725 316 898

3 .6 7 5 3 .6 7 6 3 .6 7 7 3 .6 7 8 3 .6 7 9

o . 1877176 809 4638 o . 1881 8 1 5 275 4 6 4 1 0 .1 8 8 6 4 5 6 2 9 9 4 6 4 3 0 .1 8 9 1 0 9 9 8 7 0 4 6 4 6 0 .1 8 9 5 7 4 5 9 7 7 4 6 4 8

466 024 571 107 632

2563

>.680 ) .6 8 1 >.682 1.683 1.684

0 . 1 9 0 0 3 9 4 6 0 9 4 6 5 1 145 0 .1 9 0 5 0 4 5 7 5 4 4 6 5 3 6 4 9 o . 1909699 4 ° 3 4 6 5 6 140 0 .1 9 1 4 3 5 5 543 4 6 5 8 621 0 .1 9 1 9 0 1 4 1 6 4 4661 091

3 .6 7 0 3 .6 7 1 3 .6 7 2 3 .6 7 3

1.685 0 . 1 9 2 3 6 7 5 2 5 5 1.686 o . 1 9 2 8 3 3 8 8 0 4 1.687 0 . 1 9 3 3 0 0 4 8 0 2 1.688' 0 . 1 9 3 7 6 7 3 2 3 6 1.689 0 . 1 9 4 2 3 4 4 0 9 7

1.690 1.691 1.692 1.693 '.6 9 4

0 .5 8 6 8 4 7 8 6 9 7 6 9 3 0 5 3 4 6 9 2 4 142 6917752 6 9 1 1 365 6904 979

0 .5 8 7 5 4 0 9 2 3 1 0 .5 8 8 2 3 3 3 373 0 . 5 8 8 9 2 5 1 125 0 .5 8 9 6 1 6 2 4 9 0

0 .5 9 0 3 0 6 7 4 6 9 6898 0 .5 9 0 9 9 6 6 0 6 6 6 8 9 2 0 .5 9 1 6 8 5 8 2 8 1 6885 0 .5 9 2 3 7 4 4 119 6 8 7 9 0 .5 9 3 0 6 2 5 5 8 0 6 8 7 3

6391 6389 6387 6384

2542 2531 2519

2508 2497 2486 2476 2464

0 .5 9 7 1 7 6 6 581 6 8 3 4 0 .5 9 7 8 6 0 1 4 7 6 68 2 8 0 .5 9 8 5 4 5 0 0 1 5 6 8 2 2 0 .5 9 9 2 2 5 2 1 9 9 6 815 0 .5 9 9 9 0 6 8 0 3 1 6 8 0 9

6358 6356

0 .6 0 1 9 4 7 7 4 4 3 0 .6 0 2 6 2 6 7 894 0 .6 0 3 3 0 5 2 0 0 7

4694 529

639 3

6370 6368 6366

4668434 243' 4 6 7 0 861 2421 4 6 7 3 2 76 2 4 1 0

4687541 4689 880 4692 210

6395

597 6382 215 6 3 7 9 838 6377 461 6 3 7 5 087 6 3 7 3

°-5944363

0 .( 0 0 5 8 7 7 514 0 .(0 1 2 6 8 0 6 5 1

680 074 458 829 190

6404 6402 6400 6397

0 .5 9 3 7 4 9 6 6 6 7 6 8 6 6 7 1 6 383 6 8 6 0 3 4 7 0 .5 9 5 1 2 2 3 7 3 0 6853 9 8 0 0 .5 9 5 8 0 7 7 7 1 0 6 8 4 7 6 1 6 0 .5 9 6 4 9 2 5 3 2 6 6 8 4 1 2S5

2 553

4603 549 2 4 5 3 4665 998 2442

0 .1 9 4 7 0 1 7 3 7 3 4675 0 .1 9 5 1 6 9 3 0 5 3 4 6 7 8 o . 1 9 56371 127 4 6 8 0 0 .1 9 6 1 0 5 1 5 8 5 4 6 8 2 0 .1 9 6 5 7 3 4 4 1 4 4 6 8 5

1.695 0 . 1 9 7 0 4 1 9 6 0 4 1.696 0 . 1 9 7 5 1 0 7 1 4 5 1.697 O.I979797O25 1.698 O . I 9 8 4 4 8 9 2 3 5 1.699 o . 1 9 8 9 1 8 3 7 6 4

2 575

526 124 723 325 929

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5227446 5222 226 5217012 5211 802 5206597

0.960 0.961 0.962 0.965 0.964

0.3265790 862 4995 942 209 0.7649928 0.3270786 804 4096 148 204 0.7655129 0.5275782952 4996 350 199 0.7660325 0.3280779 302 4996 546 195 0.7665516 0.3285775 848 4996 735 187 0.7670702

327 725 928 941 770

5201 398 5196 203 5191 013 5185 829 5180 648

0.965 0.966 0.967 0.968 0.969

0.3290772 583 0.3295769 505 0.3300766 601 0.3305763 873 0.3310761313

1.3827599213 1.3834507581 1.3841419 725 1.3848335 640 1.3855255 321

6908 6912 6915 6919 6923

5197 5192 5187 5182 5177

1.3862178 761 1.5869105 955 1.3876036898 1.3882971584 1.3889910007

6927194 375i 0,960 6930 943 3746 0,961 6934 686 3740 0,962 6938 423 3755 0,963 6942 155 3729 0,964

154 149 143 138 132

0.975 0.3340749 170 4998 462 0.976 0.3345747632 4 q q 8 586 0-977 0 .^ 5 0 7 4 6 3i8 4998 706 0.978 0-3355744 924 4998 819 0.979 o . 3560743 743 4998 927

127 0.7727406 116 5124 000 5125 122 0.7732530 116 5118 880 5117 117 0.7757648 996 5113 766 5112 n o 0.7742762 762 5108 656 5108 106 0.77478714i8 5103 550 5102

140 815 345 735 990

5149675 5144 530 5139590 5134255 5129 126

X

52-22 5217 5212 5207 5202

568 3779 0,955 144 5773 0,956 915 3768 o ,957 681 3762 0,958 440 3756 o ,959

4996 920 182 0.7S75883 418 5175 474 5172 1.3896852162 6945 880 4997098 176 0.7681058 892 5170 305 5167 1.3903798042 6949 601 4997 272 171 0.7686229197 5165 139 5163 1.3910747643 6953 317 4997 440 165 0.7691394336 5159 979 5157 1.1Q17700960 6957025 4997 602 159 0.7696554 315 5154825 5152 1.3924657985 6960 729 0.7701709 0.7706858 0.7712003 0.7717142 0.7722276

A2

68Sq 3QQ 3808 0,950 6893 204 3802 0,951 6897 004 3796 0,952 6900 797 5790 0,953 6904 585 5785 o ,954

0.970 0 . 33T5758 9I 54997 759 0.971 0.3320756 674 4997 9“ 0.972 o .3 3 25754 585 4998 056 0-971 0.3330752 641 4998 197 0.974 0.3335750 858 4998332

0.980 0.981 0.982 0.983 0.984

Aa

1.3795114 224 1.3800003 623 1.3806896 827 1.5815795851 1.3820694 628

0.7597627 549 5253 618 5247 0. 7602881167 5248 575 5242 0.7608129 540 5245 134 5237 0.7613372 674 5237900 5232 0.7618610 574 5232 670 5227

0.950 0.3215844 054 4993 563 o . 95i 0.5220837 617 4993 827 0.952 0.5225831 444 4994 085 0.955 0.3230825 529 4994 337 0,954 0.3235819 866 4994 583

V l+x*

5147 5142 5137 5132 5127

0.3565742 670 4999 031 IOI 0.7752974 968 5098 451 5096 0.5570741 701 4999128 95 0.7758073 419 5093 355 5092 0.5375740829 4999 221 90 0.7763166 774 5088 266 5087 0.3380740 050 4999 307 85 0.7768255 040 5083 181 5082 0.5585739 357 4999 390 80 0.7775338 221 5078 IOI 5078

5723 0,965 3718 0,966 3712 0,967 3706 0,968 3701 0,969

1.3931618 714 6964 428 3695 o,97o 1.3938583 142 6968 120 3690 0,971 1.3945551262 6971 807 3685 0,972 1.3952525009 6975 489 3679 o ,973 1.3959498 558 6979 165 3673 o ,974 1.3966477723 1.3973460559 1.3980447060 1.3987437221 1.3994431035

6982 836 6986 501 6990 161 6993 814 6997464

1.4001428 1.4008429 1.4015434 1.4022442 1.4029454

499 605 349 726 729

7001 106 3640 0,980 7004 744 3635 0,981 7008 577 3630 0,982 7012 003 3624 0,983 7015 625 3619 0,984

;6c8 o ,975 3662 0,976 3657 o,977 3651 0,978 3646 o ,979

0.985 0.3390738 747 4999467 0.986 0.3395758214 4999538 0.987 0.3400737 752 4999 604 0.988 0.3405737 356 4999 665 0.989 0.3410737021 4999 721

74 0.7778416 322 5073 025 68 0.7783489547 5067956 63 0.7788557303 5062 891 58 0.7793620 194 5057831 53 0.7798678 025 5052 776

5072 5067 5062 5057 5055

1.4036470 354 1.4043489595 1.4050512 446 1.4057538903 1.4064568 959

7019 241 3613 0,985 7022 851 3608 0,986 7026457 3603 0,987 7030 056 3597 0,988 7033651 359i 0,989

0.990 0.3415736 742 4999 772 0.991 0.3420756 514 4999 818 0.992 0.3425756332 4999 858 0-993 0.3430736 190 4999 893 0,994 0.3435736083 4999 924

48 0.7805730 801 43 0.7808778 526 37 0.7813821207 33 0.7818858 848 20 0.7823891 454

5047 725 5047

5042 5057 5052 5027

1.4071602 610 1.4078639 849 1.4085680 672 1.4092725 074 1.4099773 048

7037239 5586 0,990 7040 823 3581 o,99i 7044 402 3575 0,992 7047 974 3570 o ,993 7051 542 35°5 0,994

5042 681 5037641 5032 606 5027576

0.995 0.3440736 007 4999 949 22 0,7828919 030 5022 551 5023 1.4106824 590 0.996 0.3445735 956 4999 969 18 0.7835941581 5017530 5017 1.4113879 694 0.997 0.3450735 925 4999 985 13 0.7838959 111 5012 516 5012 1.4120938354 0.998 0.3455735 910 4999 994 7 0.7843971627 5007 506 5007 1.4128000 566 0-999 0.3460735 904 4999 999 —n2 0.7848979 133 5002 501 5002 1.4135066 325 0.7853981 634 4997 50i 4998 i .4142135 624 X,000 0.3465735 903 4999 999

110

7055 104 7058 660 7062 212 7065 759 7069 299 7072 834

3559 o ,995 3554 0,996 3549 0,997 3543 0,998 3538 o,999 3533 1,000

Table for computing the coefficient M >x (1—x) for quadratic interpolation

.

0

2

1

3

4

0. 0015 0084 0131 0x78 0224

9

8

0237 0282 0325 0368 0 ,0 9 0409

0242 0286 0330 0372 04x4

0246 0291 0334 0376 0418

0251 0395 0338 0381 0422

0355 0 2 6 0 030 0 0304 03 4 3 0347 0385 0389 0426 0430

0264 0269 0373 0308 0313 03x7 0351 0 3 5 5 0360 0393 0 3 9 7 040 X 0434 0438 0 4 4 3

0 ,1 0 0 ,1 1 0 ,1 2 0 ,1 5 0 ,1 4

0450 0489 0528 0565 0602

0454 0493 0532 0569 0606

0458 0462 0 497 0501 0536 0539 0573 0577 0609 0613

0466 0470 0505 0509 0 5 4 3 0547 0580 0584 0616 0620

0474

o ,i5 0 ,1 6 0 ,1 7 0 ,1 8 0 ,1 9

0637 0672 0705 0738 0769

0641 0 644 0675 0 6 7 9 0 7 0 9 07x2 0741 0744 0773 0776

0648 0682 0715 0748 0779

065 X 0686 0719 0751 0782

0655 0658 0662 0689 0692 0696 0 7 3 2 0725 0728I 0 7 5 4 0 7 5 7 0760 0785 0788 0791

0 ,2 0 0 ,2 1 0 ,2 2 0 ,2 3 0 ,2 4

0800 0829 0858 0885 0912

0803 0832 0861 0888 09x5

0806 0835 0864 0891 0917

0809 0838 0866 0894 0920

0812 084X 0869 0896 0922

0815 0844 0872 0899

0 ,2 5 0 ,2 6 0 ,2 7 0 ,2 8 0 ,2 9

0937 0962 0985 1008 1029

0940 0964 0988 lO IO IO 32

0943 0967 O99O 1012 1034

0943 0 9 4 7 0969 O 992 0 9 9 5 1015 X0 I 7 1 0 3 6 XO38

0950 0974 0997 1019 1040

0 ,0 5 0 ,0 6 0 ,0 7 9 ,0 8

oqji

0, 0030 0079 0127 0174 0219

7

0, 0010 0059 0108

0, 0015 0064 0112 0155 0 1 6 0 0201 0 206

0, 0025 0074 0122 0x69 0215

6

0, 0, 0 0 0 0 0005 0049 0054 0098 0103 0145 0 1 5 0 0192 0197

0 ,0 0 0 ,0 1 0 ,0 2 0 ,0 3 o ,o 4

0, 0020 0069 0117 0x64 02x0

5

0, 0040 0088 0136 0183 0228

0, 0045 0093 0x41 0187 0233

0478 0482 0517 0520 0 5 5 4 0558 059X 0 5 9 5 0627 0630

0276 0321 0364 0405 0446 0486 0534 0562 0598 0634

n

10 0, 0049 0 ,9 9 0098 0 ,9 8 o ,9 7 0192 0 ,9 6 0237 0 ,9 5

0282 0 ,9 4 o ,9 3 0 368 0 ,9 2 0 409 0 ,9 1 0 4 5 0 0 ,9 0

0665 0699 0733 0763 0794

0669 0672 0702 0705 °7 3 5 0738 O 766 O 769 0 7 9 7 O8OO

0 ,8 4 0 ,8 3 0 ,8 2 0 ,8 1 o ,8 o

0818 0821 0847 0850 0875 0 8 7 7 0902 0904 0935 0 9 2 7 0 9 3 0

0824 0852 0880 0907 0932

0827 0829 0835 0 858 0883 0885 0 9 0 9 0912

0 ,7 9

0935

o ,7 5

0952 0 9 5 5 0976 0979 0 9 9 9 1001 1021 1023 1042 1044

0957

0937

0962 o ,7 4 o ,7 3 1008 0 ,7 2 1029 0 ,7 1 x oso 0 ,7 0

1066 1084 1102 1119 1134

1068 1086 X104 1120 1136

X069 1088 1105 1122 1137

1149 1x63 1176 1187 X I9 7 1 1 9 8

1151 1164 1177 x i8 8 1199

X152 0 , 6 4 1x65 0 , 6 3 1178 0 ,6 2 x i 8 q 0 ,6 1 1200 0 ,6 0

1x37 1139 1 1 5 2 1153 1167 1 1 6 5 1178 1179 1 1 8 9 1191

1140 1142 1156 1168 1x69 1x80 1182 1 1 9 2 1193

H43

1145

II5 8 1171 1183 1194

1159 1172 1184 X195

1x46 1160 X173 1x85 1x96

1148 1162 1x74 1186

0 ,4 2 o ,4 3 o ,4 4

1 2 0 0 1201 1210 1 2 1 0 121Q 1225 1 2 2 6 I2 3 2 1233

1202 1211 1220 1227 X3 3 3

1203 1212 1220 1228 1334

1204 1213 1221 1228 1234

1206 1215 1222 1223 1 2 2 9 I.23O 1335 1235

1207 1216 1223 1230 1236

1208 1216 1224 la ^ l 1336

1209 1217 1225 I2 3 I 1237

1209 X2 X8 1225 1232 1337

o ,4 5 0 ,4 6 o ,4 7 0 ,4 8 o ,4 9

•2 3 7 1242 1245 1248 1249

1238 1242 X246 1248 1250

1238 1243 1246 1248 1250

1339 1239 1243 1 2 4 4 1246 1247 1349 1349 1250 1250

1240 1244 1247 X2 4 9 1250

1340 1344 1347 1349 1250

1241

1241 1245 1246 1249 1250

1242 1245 1248 1249 1250

1242 o ,5 4 1345 o , 5 3 1248 0 ,5 2

10

9

,5

4

3

o ,3 7 0 ,3 8 ° ,3 9

0 ,4 0 o ,

4x

120Q

8

7

In ( _ 1) _

6

1205

1214

1345 1247 1249 1250

= 3,1415926536 i

2

1

6 ,9 0 7 755378 985

4

9 ,2 1 0 340371 978

5

11,512925 4 6 4 9 7 0

6

13,815 5 x0 5 5 7 9 6 4

7

16,118 095 6 5 0958

8

1 8 ,4 2 0 6 8 0 743 953

9

20,723 265 8 5 6 94 6

10 23,025 8 5 0 9 2 9 9 4 0

'3

29 ,93 3

208922

i4

32 ,23 6 191 301 916

0 9 8 5

1062 1064 x o 8 i X083 1099 1100 1110 1117 XX31 1 x 3 3

1 x 3 $

3

12 2 7 ,6 3 1 0 2 1 1 1 5 928

1060 1079 1097 1114 1130

3S

4 ,6 0 5 1 7 0 1 8 5 988

11 2 5 ,3 2 8 4 3 6 0 2 2 9 3 4

1058 1077 1095 IT 1 2 XX28

0 ,3 6

2

o ,7 7 0 ,7 6

1054 1056 1075 1 0 9 2 1093 1109 1111 1x25 1 1 2 7

° >

2 ,3 0 2 5 8 5 092 994

0 ,7 8

0 ,3 0 1050 1052 0 , 3 1 10691 1071 0 , 3 2 1 0 8 8 IO 9 0 ° > 3 3 1105 1 1 0 7 1122 1124 o ,3 4

X 073

1

0335

0 ,8 9 0 ,8 8 0 ,8 7 0 ,8 6 0 ,8 5

0960 0981 0 9 8 3 1004 1006 1025 1 0 2 7 1046 1048

10n

0145

0489 0528 0565 0602 0637

0513 0551 0588 0623

In

0 ,6 9 0 ,6 8 0 ,6 7 0 ,6 6 0 ,6 5

o ,5 9 0 ,5 8 o

15 34.538 776 394 910 16

36,841 361 4 8 7904

17 3 9 ,1 4 3 9 4 6 5 8 0 8 9 8 18 4 1 , 4 4 6 5 3 ! 673 892

*9

4 3 ,7 4 9 116 766 886

20 46,051 701 859 880

21

4 8 ,3 5 4 2 8 6 9 5 2 8 7 4

22

5 0 ,65 6 8 7 2 0 4 5 868

33

52,959 457 138 862

24

5 5 , 2 6 2 0 4 2 2 3 x 856

,5 7

0 ,5 6 o ,5 5

'3 4 9 0 , 5 1 X 250 0 , 5 0

35

5 7 ,5 6 4 6 2 7 3 2 4 8 5 0

0

In < = - < = 1,5707963268 i

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