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Series with e^x

  1. Dec 14, 2012 #1
    You have:

    Ʃ(n+1)/n! x^n = (1+x)e^x

    Is it in general true with a polynomium that:

    ƩP(n)/n! x^n = P(x)e^x

    ?
     
  2. jcsd
  3. Dec 14, 2012 #2
    That's easy to check. What is ƩP(n)/n! x^n for P(n) = n(n-1)?
     
  4. Dec 14, 2012 #3
    uhhh I don't know. Is that a series I should know? :(

    Edit: Wait if you let the factorials cancel out you get: Ʃx^n/(n-2)! but doesn't get me furhter
     
  5. Dec 14, 2012 #4

    Ray Vickson

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    Yes, it does (or should); you just need to write things out more explicitly:
    [tex] e^x = 1 + x + \frac{1}{2!}x^2 + \frac{1}{3!} x^3 + \frac{1}{4!} x^4 + \cdots.[/tex] Now write out ##\Sigma\: n(n-1) x^n/n!## in a similarly-detailed way.

    Using the Ʃ notation saves time and writing after you are thoroughly familiar with the techniques, but until then you might do better to avoid relying on it.
     
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