# How do you find a power series representation for #e^(-x^2)# and what is the radius of convergence?

##### 1 Answer

Oct 24, 2015

Use the power series for

#e^(-x^2) = sum_(n=0)^oo (-1)^n/(n!) x^(2n)#

with infinite radius of convergence.

#### Explanation:

#e^t = sum_(n=0)^oo t^n/(n!)#

with infinite radius of convergence.

Substitute

#e^(-x^2) = sum_(n=0)^oo (-x^2)^n/(n!)=sum_(n=0)^oo (-1)^n/(n!) x^(2n)#

Which will converge for any