# Power series expansion of an exponential

1. ### t_n_p

581
1. The problem statement, all variables and given/known data

expand the exponential term in the equation y=2[e^{x+(x²/2)}-1] as a power series

2. Relevant equations

on wikipedia I found this...

3. The attempt at a solution
Do I substitute x+(x²/2) as "x" in the above formula and proceed as normal or must I do something different?

2. ### dirk_mec1

688
Yes, just substitute.

3. ### HallsofIvy

40,214
Staff Emeritus
Don't forget to multiply each term by 2 and subtract 1 from the constant term.

4. ### tiny-tim

26,055
And brush your teeth!

5. ### t_n_p

581
Thanks for the quick replies.
Using "x" = x+x²/2

I get y=2{1 + x + x²/2 + (x+x²/2)²/2 +.....}-1