1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Power series help

  1. Jan 31, 2007 #1
    How do I multiply power series?

    1. The problem statement, all variables and given/known data
    Find the power series:
    [tex] e^x arctan(x) [/tex]

    2. Relevant equations

    [tex] e^x = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} [/tex]

    [tex] arctan(x) = 0 + x - \frac{x^3}{3} + \frac{x^5}{5} - \frac{x^7}{7}[/tex]
    3. The attempt at a solution

    So do I multiply 1 by 0, x by x and so forth? Or do I go 1 by 0, 1 by x? Or is there another way?
    Last edited: Jan 31, 2007
  2. jcsd
  3. Jan 31, 2007 #2
    You have to multiply 1 by the whole acrtan series, x by the whole arctan series, and so on. There might be a way to simplify it though. Wikipedia has this under "power series"

    [tex]f(x)g(x) = \left(\sum_{n=0}^\infty a_n (x-c)^n\right)\left(\sum_{n=0}^\infty b_n (x-c)^n\right)[/tex]

    [tex] = \sum_{i=0}^\infty \sum_{j=0}^\infty a_i b_j (x-c)^{i+j}[/tex]

    [tex] = \sum_{n=0}^\infty \left(\sum_{i=0}^n a_i b_{n-i}\right) (x-c)^n [/tex]
  4. Jan 31, 2007 #3
    So I kind of treat it like F.O.I.L.?
  5. Jan 31, 2007 #4

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Sort of. FOIL is the distrubutive law for (binomial)X(binomial). Here, you've got two infinitely long "polynomials". Obviously, you won't be able to write out all of the terms. :tongue:
  6. Jan 31, 2007 #5
    Awesome, I think I got it, I only had to take it out to the [tex] x^5 [/tex] term.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Power series help
  1. Power Series Help (Replies: 6)

  2. Power series help (Replies: 6)

  3. Power series help (Replies: 5)

  4. Power Series help. (Replies: 4)