Question

How would I find the series expansion for,

Answer 1

\[/\large \int\limits_{0}^{x} e ^{-t ^{2}} = a _{0} + a _{1}x + a _{2}x ^{2} + a _{3}x ^{3}+...\]

Answer 2

\[/\large e ^{-t ^{2}} = 1 + (-t ^{2}) + (-t ^{2})^{2}\]
etc.
would i integrate that?

Answer 3

actualyl forgot the factorials

Answer 4

yes, integrate term by term, then write it in summation notation to make it look pretty