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-   -   Power series expansion of an exponential (http://www.physicsforums.com/showthread.php?t=251732)

 t_n_p Aug24-08 03:59 AM

power series expansion of an exponential

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 Aug24-08 04:02 AM

Re: power series expansion of an exponential

Quote:
 Quote by t_n_p (Post 1846269) 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 Aug24-08 04:08 AM

Re: power series expansion of an exponential

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

 tiny-tim Aug24-08 04:25 AM

Quote:
 Quote by HallsofIvy (Post 1846273) Don't forget to multiply each term by 2 and subtract 1 from the constant term.

 t_n_p Aug24-08 05:03 AM

Re: power series expansion of an exponential

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!

 Defennder Aug24-08 06:57 AM

Re: power series expansion of an exponential

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

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