# Power series expansion of an exponential

1. Aug 24, 2008

### 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 [Broken]

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?

Last edited by a moderator: May 3, 2017
2. Aug 24, 2008

### dirk_mec1

Yes, just substitute.

3. Aug 24, 2008

### HallsofIvy

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

4. Aug 24, 2008

### tiny-tim

5. Aug 24, 2008

### 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

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!

6. Aug 24, 2008

### Defennder

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