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? 
Re: power series expansion of an exponential
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Re: power series expansion of an exponential
Don't forget to multiply each term by 2 and subtract 1 from the constant term.

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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 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! 
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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