Evaluate integral as a power series + find radius of conv.

• December 4th 2007, 07:57 AM
grib90
Evaluate integral as a power series + find radius of conv.
Evaluate integral as a power series and find the radius of convergence.

f(x) = [e^(-t^3)]dt

Very few helpful examples of these in my book so any help is appreciated.
• December 4th 2007, 08:14 AM
ThePerfectHacker
Quote:

Originally Posted by grib90
Evaluate integral as a power series and find the radius of convergence.

f(x) = [e^(-t^3)]dt

Very few helpful examples of these in my book so any help is appreciated.

$\int e^{-t^3} dt = \int 1 - t^3 + \frac{t^6}{2!}-\frac{t^9}{3!}+... dt$
• December 4th 2007, 08:44 AM
grib90
Quote:

Originally Posted by ThePerfectHacker
$\int e^{-t^3} dt = \int 1 - t^3 + \frac{t^6}{2!}-\frac{t^9}{3!}+... dt$

Now I have

$\int e^{-t^3}=\int \sum_{n=0}^\infty\frac{(-1)^n*t^{3n}}{n!}*dt = C + \sum_{n=0}^\infty {(-1)^n}$

Now how do I deal with that factorial when integrating?
• December 4th 2007, 10:11 AM
topsquark
Quote:

Originally Posted by grib90
$\int e^{-t^3}=\int \sum_{n=0}^\infty\frac{(-1)^n*t^{3n}}{n!}*dt = C + \sum_{n=0}^\infty {(-1)^n}$