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Power series expansion of an exponential

  1. Aug 24, 2008 #1
    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...
    [​IMG]

    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. jcsd
  3. Aug 24, 2008 #2
    Yes, just substitute.
     
  4. Aug 24, 2008 #3

    HallsofIvy

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    Don't forget to multiply each term by 2 and subtract 1 from the constant term.
     
  5. Aug 24, 2008 #4

    tiny-tim

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    And brush your teeth! :biggrin:
     
  6. Aug 24, 2008 #5
    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!
     
  7. Aug 24, 2008 #6

    Defennder

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    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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