1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Maclaurin power series

  1. Nov 27, 2006 #1


    User Avatar

    I was hoping someone could check my work:

    Find the maclaurin power series for the function:

    a. f(x)=1/(4x^2+1)

    b. f(x)= [tex]\int[/tex] e^-x^2 dx

    For a I got [tex](-1)^n*2nx^n[/tex]. For b I dont know where to start.
    Last edited: Nov 27, 2006
  2. jcsd
  3. Nov 27, 2006 #2


    User Avatar

    For b I can get the approx to be


    So i get (x^-2n)/n!
  4. Nov 27, 2006 #3
    1 (a) [tex] f(x) = \frac{1}{1+4x^{2}} [/tex]

    This is equaled to [tex] \sum_{n=0}^{\infty} (-4)^{n}x^{2n} [/tex]

    (b) [tex] e^{x} = \sum_{n=0}^{\infty} \frac{x^{n}}{n!} [/tex]

    Thus [tex] e^{-x^{2}} = \sum_{n=0}^{\infty} (-1)^{n}\frac{x^{2n}}{n!} [/tex] and

    [tex] \int \sum_{n=0}^{\infty} (-1)^{n}\frac{x^{2n}}{n!} = \sum_{n=0}^{\infty} (-1)^{n}\frac{x^{2n+1}}{(2n+1)n!} [/tex]
  5. Nov 27, 2006 #4


    User Avatar

    Thanks for the help. I just got b and was coming back to post my answer.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook