Results 1 to 5 of 5
Like Tree1Thanks
  • 1 Post By emakarov

Math Help - Representation of Power Series Problem

  1. #1
    Junior Member
    Joined
    Aug 2012
    From
    Texas
    Posts
    49

    Representation of Power Series Problem

    Hey guys, I am having a bit of difficulty with this power series problem:

    \ln\sqrt\frac{1+2x}{1-2x}

    Basically I need to find a power series representation for this function. First I tried breaking this problem down through properties of logarithm:

    \frac{1}{2}[ln(1+2x) - ln(1-2x)]

    Then afterwards, I tried various steps and (random) methods to try and solve this problem. As of right now I am completely stuck, and I have no idea how to further continue this problem.

    Any feedback and help on this problem would be greatly appreciated.

    Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,559
    Thanks
    785

    Re: Representation of Power Series Problem

    Have you tried using Maclaurin series for ln?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Sep 2012
    From
    Washington DC USA
    Posts
    525
    Thanks
    147

    Re: Representation of Power Series Problem

    First do the series for ln(1+u) about u = 0. Then plug in u=2x and u=-2x and subtract them. You'll get a lot of cancellation and simplification.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Aug 2012
    From
    Texas
    Posts
    49

    Re: Representation of Power Series Problem

    Quote Originally Posted by emakarov View Post
    Have you tried using Maclaurin series for ln?
    Would you need to use the Mclaurin series for this. I just started learning about the Taylor/Mclaurin series, and this problem seems a bit complicated to use the Mclaurin series method.

    Quote Originally Posted by johnsomeone View Post
    First do the series for ln(1+u) about u = 0. Then plug in u=2x and u=-2x and subtract them. You'll get a lot of cancellation and simplification.
    Thanks! So basically, I can ignore the 1/2 (from the square root function) and just focus on the ln(1 + u) and simplify the problem, and then later factor in the 1/2?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,559
    Thanks
    785

    Re: Representation of Power Series Problem

    Mclaurin series is Taylor series about 0.

    Quote Originally Posted by Beevo View Post
    Thanks! So basically, I can ignore the 1/2 (from the square root function) and just focus on the ln(1 + u) and simplify the problem, and then later factor in the 1/2?
    Yes.
    Thanks from Beevo
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Power Series Representation Problem
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 18th 2010, 06:52 PM
  2. power series representation!
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 19th 2009, 08:08 PM
  3. power series representation #2
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 12th 2009, 06:37 PM
  4. power series representation problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 22nd 2007, 11:30 PM
  5. power series representation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 8th 2007, 10:34 AM

Search Tags


/mathhelpforum @mathhelpforum