TABLE ERRATA 4> -.8 6 9 9

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TABLE ERRATA 397.—Paul F. Byrd & Morris

D. Friedman,

Engineers and Physicists, Springer-Verlag, The following corrections

Handbook of Elliptic Integrals for Berlin, 1954.

should be made in the table entitled

Values of the

Function KZiß, k), on pp. 336-343. sin 1 k

ß

15° 40°

44° 57° 64°

for .027204 .196336 .171978 .124059 1.982530 .548499 1.229612 2.154030 1.931185 2.635400 .616197 3.351047 2.081462

73° 63° 87° 22° 44° 79° 73° 8° 71° 86°

85° 87° 88° 89°

read

.027203 .196349 .171980 .124061 1.982526 .558435 1.229589 2.153771 1.930751 2.635330 .616207 3.350992 2.081437 Henry E. Fettis James C. Caslin

Applied Mathematics Laboratory Aerospace Research Laboratories Wright-Patterson Air Force Base, Ohio

Editorial

note:

An additional

serious error in this table was noted by D. Caligo (MTAC,

v. 13, 1959, p. 141, MTE 269). For further notices of errata in this book, see Math. Comp.,

v. 18, 1964, p. 532, MTE 352, and p. 687, MTE 359.

398.—Henry E. Fettis

& James C. Caslin, Tables of Elliptic Integrals of the First,

Second and Third Kind, Report ARL 64-232, Aerospace Research Wright-Patterson Air Force Base, Ohio, December, 1964.

Laboratories,

In Table III (pp. 44-93), corresponding to k2 = 1.00, the following additive corrections should be made, in units of the last decimal place.

4> a

65.0°

70.0°

75.0°

-1.0 -.9

80.0°

82.5°

85.0° 1

2

-.8

2 2

—.7 -.6 —.5

2

2 2

-.4 639

87.5° 6 7 7 7

9 9 10

640

ERRATA

-.3 -.2 -.1 + .1 4-.2 + .3 4- .4 4-.5 4-.6 + .7 4-.8 4-.9 1.0

1

1

1

1 114 1 2

1 111

1 1

2 2

1 13 1

1

4

1 1 2 1

3 2 3 3

2 3 3 4 4 6 10

4 5 7 8 10 14 27 1

10 10 11 14 16 18 22 26 32 42 63 122 3

These errors in the table of 10D values of the elliptic integral of the third kind are attributable to a programming error, which resulted in the value of k~ being set

equal to 1 — 10~ instead of 1.

Henry E. Fettis Applied Mathematics Research Laboratory Wright-Patterson Air Force Base, Ohio

Editorial

note : For a review of these tables see Math. Comp., v. 19,1965, p. 509, R MT 81

399.—Milton Abramowitz & Irene A. Stegun, Editors, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards, Applied Mathematics Series, No. 55, U. S. Government

Printing Office, Washington,

D. C, third printing, March 1965.

On p. 333, formula 8.2.7 should read

iz1 - lY'^-^Q/iz)

-1/2r -i/2

[j

.(z2 -

l)l/2J

(Itt)1'2!^

+ p. + 1)

and the left side of formula 8.2.8 should read

e-i-i/t |_(z, Jiji/iJOn p. 334, the left side of formula 8.6.11 should read —Qv iz). On p. 335, in formula 8.8.2 the factor iz2 — l)-"'2 on the right side should be replaced by iz2 -

1)"/2.

Henry E. Fettis Applied Mathematics Research Laboratory Wright-Patterson Air Force Base, Ohio

On p. 783, in formula 22.9.8 the third column should read (1 — In R")/2, and in formula 22.9.11 the third column should read R~\l — xz -\- R)~112.

Van E. Wood Battelle

Memorial

Columbus,

Ohio

Institute

641

ERRATA

Recalculation of the coefficients in the Maclaurin series for l/r(z) to more than 25D has revealed the following corrections to be required in the 16D table in 6.1.34 on p. 256. The final decimal digits in ck corresponding to k = 3, 8, 10, 12, 16, and 17 should each be increased by a unit ; the final digits in en and c24should each be decreased by a unit, while the value c2s should be decreased by two final units. Also, the sign of c26should be changed to minus. This supplements and emends the corrections made by Isaacson and Salzer

iMTAC, v. 1,1943, p. 124, MTE 19) in the corresponding original table of Bourguet

¡Acta Math., v. 2, 1883, pp. 261-295).

J. W. W. Editorial note: An independent calculation of en shows that the value, 206, given in the NBS Handbook is correct—contrary to the assertion made in MTE 393. In fact c23 =

-0.0,3 20 58326 05356 479

400.—A. Erdélyi, Transcendental

W. Magnus, Functions,

F. Oberhettinger

Volume 2, McGraw-Hill

& F. G. Tricomi,

Higher

Book Co., New York, 1953.

On p. 187, the right side of equation (34) should read Tn+mix)

4- Tn-mix).

Van E. Wood 401.—A. Erdélyi, W. Magnus, F. Oberhettinger & F. G. Tricomi, Integral Transforms, McGraw-Hill Book Co., New York, 1954.

Tables of

In Volume I, p. 218, in transform 4.23(18), for %a, \o -f- \, recul o, a 4- §. Also, the second convergence condition on the right should read Re p > 2 | Re X | if m = n — 1. In Volume II, pp. 128-129, in transform 10.2(9), the denominator parameters in

the first iF2 should be 1 — p. — (p + v)/2, 1 — p. — (p — v)/2, while the numerator parameter

in the second iF2 should be (p -f- v)/2.

In Volume II, p. 153, in transform 10.3(88), for —\x2, read \x2. Also change the convergence

conditions

on the right to read

Re y > 0 if p < q — 1; Rey > 2 | Re X | if p = q - 1. Van E. Wood 402.—G. E. Roberts

& H. Kaufman,

Table of Laplace Transforms, W. B. Saunders,

Philadelphia, Pennsylvania, 1966.

On p. 116, in transform 33.2.1(18), for c/2, (c 4- l)/2, read c, c + §. Also, the last convergence condition should read Re s > 2 | Re A;| if p = a — 1. On p. 112, transform 32.1(3) is a special case of the preceding, and the convergence

conditions

should accordingly

be

Res > 2 | Rec|, Res > 0,

q = p + 1;

q > p + 1. Van E. Wood

642

ERRATA

403.—D. H. Lehmer, Council, National

Guide to Tables in the Theory of Numbers, National Research Academy of Sciences, Washington, D. C, 1941, reprinted

1961. On p. 162, in section 2, [fi], it is erroneously stated that 108 4- 2271, 108 + 4291, and I08 4- 4909 should be deleted from the list of primes given on pp. 97-98 of Tavole di Numeri Primi entro Limiti Diversi e Tavole Affini, by L. Poletti, Milan, 1920. In fact, these numbers are prime. There exists an additional error in Poletti's table; namely, 108 4~ 9513 is not

prime, since it is divisible by 1531.

M. F. Jones M. Lal Memorial

University

of Newfoundland

St. John's, Newfoundland Canada Editorial note: The primality of the first three numbers cited can be verified by consulting C. L. Baker & F. J. Gruenberger, The First Six Million Prime Numbers, The Micro-

card Foundation,

Madison, Wisconsin, 1959. (See Math. Comp., v. 15, 1961, p. 82, RMT 4.)

404.—D. N. Lehmer, List of Prime Numbers from 1 to 10,006,721, Publication No. 165, Carnegie Institution

of Washington,

Washington,

D. C, 1914; reprinted

by Hafner Publishing Co., New York, 1956. A table of the Riemann function Pix) is given on pp. xiii-xvi. The entries therein should each be decreased by a unit for the following 11 values of x :

750,000 5,050,000 9,750,000

1,000,000 6,350,000 9,850,000

2,400,000 9,250,000 9,950,000

3,450,000 9,650,000

and the entry corresponding to x = 4,700,000 should be increased by a unit. In the same table the columns headed "Tchebycheff" do not constitute, as the author erroneously states (p. ix), a tabulation of

f

•'2

but of

Liix) = lim /

e-»o Jo

dy/hi y, di//In y 4- /

J\-t

dy/In y.

(The same error occurs in D. C. Mapes, "Fast method for computing

the number of

primes less than a given limit," Math. Comp., v. 17, 1963, pp. 179-185.) These tabular

values of Liix)

should be decreased by a unit for the following 11 values

of x:

650,000 4,550,000 8,350,000

1,200,000 5,350,000 8,450,000

2,150,000 5,550,000 8,800,000

4,400,000 8,200,000

and the entry for x = 9,950,000 should be increased by a unit.

M. F. Jones M. Lal

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TABLE ERRATA 4> -.8 6 9 9

TABLE ERRATA 397.—Paul F. Byrd & Morris D. Friedman, Engineers and Physicists, Springer-Verlag, The following corrections Handbook of Elliptic Inte...

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