Question

How do you find the power series representation for the function `f(x)=e^(x^2)` ?

Answer 1

Since

`e^x=sum_{n=0}^infty{x^n}/{n!}`,

by replacing `x` by `x^2`,

`e^{x^2}=sum_{n=0}^infty{(x^2)^n}/{n!}=sum_{n=0}^infty{x^{2n}}/{n!}`.

I hope that this was helpful.