Results 1 to 3 of 3

Math Help - power series representation

  1. #1
    Member
    Joined
    Oct 2010
    Posts
    127

    power series representation

    What is the power series expression for f(x)=x^2sin(x). Find the radius of convergence too.

    I know that the power series of sinx is (-1)^n (x^(2n+1))/(2n+1)! But what about the x^2? Do you just take the derivative of it?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,402
    Thanks
    1291
    If \displaystyle \sin{x} = \sum_{n = 0}^{\infty}\frac{(-1)^nx^{2n+1}}{(2n+1)!}

    then \displaystyle x^2\sin{x} = x^2\sum_{n = 0}^{\infty}\frac{(-1)^nx^{2n+1}}{(2n+1)!} = \sum_{i=0}^{\infty}\frac{(-1)^nx^{2n + 3}}{(2n+1)!} (from the Distributive Law).

    To check the radius of convergence use the ratio test.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    If...

    \displaystyle \sin x= \sum_{n=0}^{\infty} (-1)^{n}\ \frac{x^{2n+1}}{(2n+1)!} (1)

    ... multiplying both therms of (1) by x^{2} You obtain...

    \displaystyle x^{2}\ \sin x= \sum_{n=0}^{\infty} (-1)^{n}\ \frac{x^{2n+3}}{(2n+1)!} (2)



    Merry Christmas from Italy

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Power Series Representation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 25th 2010, 01:19 PM
  2. power series representation!
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 19th 2009, 07:08 PM
  3. power series representation.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 4th 2009, 05:57 PM
  4. Power series representation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 5th 2008, 12:17 PM
  5. power series representation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 8th 2007, 09:34 AM

Search Tags


/mathhelpforum @mathhelpforum