Results 1 to 2 of 2

Math Help - Laurent Series

  1. #1
    Junior Member
    Joined
    Feb 2007
    Posts
    70

    Laurent Series

    I'm just learning Laurent series. Could someone help me with this:

    Find the Laurent series for the function z/[(z+1)(z+2)] in the following regions:
    |z| < 1, 1 < |z| < 2, and |z| < 2.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    TD!
    TD! is offline
    Senior Member
    Joined
    Jan 2006
    From
    Brussels, Belgium
    Posts
    405
    Thanks
    3
    Laurent expansions about z = 0, I suppose?
    With partial fractions, you can rewrite:

    z/((z+1)(z+2)) = 2/(z+2) - 1/(z+1)

    You can now use the known Taylor series for |z| < 1. Watch out, you'll need a subtle manipulation for the other intervals, in order to make sure that the Taylor series still converge.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Laurent Series
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: September 17th 2011, 12:46 AM
  2. Laurent Series/ Laurent Series Expansion
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 5th 2010, 08:41 PM
  3. Laurent Series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 27th 2010, 02:34 PM
  4. Laurent series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 13th 2009, 12:10 PM
  5. Laurent Series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 17th 2007, 09:43 AM

Search Tags


/mathhelpforum @mathhelpforum