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

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Answer 1 · 2014-10-05T13:21:51

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.

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