# Thread: Integrating the e^{x^2} series...?

1. ## Integrating the e^{x^2} series...?

What is the series representation of $\displaystyle e^{x^2}$, and how do you do it? I want to integrate the series, considering I can't integrate the expression.

Thanks for your help!

2. ## Re: Integrating the e^{x^2} series...?

$\displaystyle \int e^{x^2}dx$:
You cannot get a primitive function expressed in elementary functions. You can look for: error function, I think there's information enough about this integral .

3. ## Re: Integrating the e^{x^2} series...?

Originally Posted by Polyxendi
What is the series representation of $\displaystyle e^{x^2}$, and how do you do it? I want to integrate the series, considering I can't integrate the expression.
$\displaystyle e^t=\sum_{n=0}^{+\infty}\dfrac{t^n}{n!}\;(\forall t\in\mathbb{R})\Rightarrow e^{x^2}=\sum_{n=0}^{+\infty}\dfrac{x^{2n}}{n!}\;\; (\forall x\in\mathbb{R})$