Power series expansion of an exponential

  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...

    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. Yes, just substitute.
  4. HallsofIvy

    HallsofIvy 41,264
    Staff Emeritus
    Science Advisor

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

    tiny-tim 26,016
    Science Advisor
    Homework Helper

    And brush your teeth! :biggrin:
  6. 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..


    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. Defennder

    Defennder 2,613
    Homework Helper

    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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