e-x-2-dx-can-we-get-a-close-form-of-this-integral-or-analytic-solution-

Question Number 64579 by Tawa1 last updated on 19/Jul/19

\int e^{x^{2}} dx

can we get a close form of this integral or analytic solution

Commented by mathmax by abdo last updated on 19/Jul/19

a t f o r m o f s e r i e

\int e^{x^{2}} d x = \int \sum_{n = 0}^{\infty} \frac{x^{2 n}}{n!} d x = \sum_{n = 0}^{\infty} \frac{1}{n!} \int x^{2 n} d x

= \sum_{n = 0}^{\infty} \frac{x^{2 n + 1}}{(2 n + 1) n!} + c w i t h r a d i u s o f c o n v e r g e n c e R = + \infty