preface to fifteenth edition

2.116 SECTION 2
x2 x3 x4 x5
ln(1 x) x ··· (1 x 1)
2 3 4 5
2 3 4 5
x x x x
ln(1 x) x ··· (1 x 1)
2 3 4 5
x 1 1 1 1 1
x 1 x 3x3 5x5 7x7
x 1 1 x 1 3 1 x 1 5
x 1 3x 1 5x 1
x 1 x 3 1 x 5
ln(a x) ln a 2 ···
3 5 7
1 x x x x
ln 2 x ··· (1 x 1)
1 x 3 5 7
ln 2 ··· (x 1or 1 x)
ln x 2 ··· (0 x )
2a x 3 2a x 5 2a x
(0 a , a x )
Series for the Trigonometric Functions. In the following formulas, all angles must be expressed
in radians. If D the number of degrees in the angle, and x its radian measure, then x
0.017453D.
3 5 7
x x x
sin x x ··· ( x )
3! 5! 7!
x2 x4 x6 x8
cos x 1 ··· ( x )
2! 4! 6! 8!
3 5 7 9
x 2x 17x 62x
tan x x ··· x
3 15 315 2835 2 2
1 x x3 2x5 x7
cot x ··· ( x )
x 3 45 945 4725
3 5 7
y 3y 5y
sin1
y y ··· (1 y 1)
6 40 112
3 5 7
y y y
tan1
y y ··· (1 y 1)
3 5 7
1 1 1 1 1
1
cos y ⁄2 sin y cot y ⁄2 tan y
Reversing a Series. If
2 3 4 5
then
2 2
y x bx cx dx ex ··· , x y by (2b
3 3 4 4 2 2 5
c)y (5b 5bc d)y (14b 21b c 6bd 3c e)y ··· , provided the latter series
is convergent.
Fourier’s Series. Let f(x) be a function which is finite in the interval from x c to x
c and whose graph has finite arc length in that interval.* Then, for any value of x between c
and c,
* If x x is a point of discontinuity, f (x 0 ) is to be defined as
1
0 ⁄2[f 1(x 0) f 2(x 0)],
where f 1 (x 0 ) is the limit of f (x) when x
approaches x 0 from below, and f 2 (x 0 ) is the limit of f(x) whenx approaches x 0 from above.