O'Reilly logo

Table of Integrals, Series, and Products, 8th Edition by Daniel Zwillinger

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

1

Elementary Functions

1.1 Power of Binomials

1.11 Power series

1.110

(1+x)q=1+qx+q(q1)2!x2++q(q1)(qk+1)k!xk+=k=0(qk)?xk

si1_e

If q is neither a natural number nor zero, the series converges absolutely for |x| < 1 and diverges for |x| > 1. For x = 1, the series converges for q > −1 and diverges for q ≤ −1. For x = 1, the series converges absolutely for q > 0. For x = −1, it converges absolutely for q > 0 and diverges for q < 0. If q = n is a natural number, the series 1.110 is reduced to the finite sum 1.111. FI II 425

1.111

(a+x)n=k=0n(nk)xkank

1.112

1. 

(1+x)1=1x+x2x3+=k=1(1)k1xk1

(see also 1.121 2)

2. 

(1+x)2=1

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required