power series expansion of an exponential

[t_n_p]

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...
http://img297.imageshack.us/img297/1088/15139862vw6.jpg

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?

[dirk_mec1]

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

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?

Yes, just substitute.

[HallsofIvy]

Don't forget to multiply each term by 2 and subtract 1 from the constant term.

[tiny-tim]

Don't forget to multiply each term by 2 and subtract 1 from the constant term.

And brush your teeth! :biggrin:

[t_n_p]

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

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

y=2x+2x²+(x^3)+(x^4)/4

I think I may have made a mistake but I cannot see where. My reason being I am supposed to show that a previously worked solution of y=2x+x²+c and the original equation y=2[e^{x+(x²/2)}-1] agree up to the first power of x only.

firstly, in the previously worked solution i am missing a coefficient of 2 for x². Secondly, why would the question ask to show that the original solution only agrees with the power series expansion of the same equation only to the power of x? It makes no sense!

[Defennder]

I suggest you post the relevant question here. We can't figure out what's wrong unless we know what the question asks.