Results 1 to 4 of 4

Math Help - Laurent Series

  1. #1
    Junior Member
    Joined
    May 2009
    Posts
    41

    Laurent Series

    I found this exercise can someone explain what I have to do it!?

    Find the expansion of f(z)=1/(z(z-1)) about the point z=1 and say for what region of the Argand plane your expansion is valid for. What therefore is the residue of this unctions at the point z=1?

    Thanks!!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    What have you tried ?

    Do you know how to get the expansion of a function at some point ?
    Do you know what a residue is ?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2009
    Posts
    41
    I just have some idea if u can explain me that is very helpful
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jan 2007
    Posts
    42
    Quote Originally Posted by NaNa View Post
    I found this exercise can someone explain what I have to do it!?

    Find the expansion of f(z)=1/(z(z-1)) about the point z=1 and say for what region of the Argand plane your expansion is valid for. What therefore is the residue of this unctions at the point z=1?

    Thanks!!

    take u = z-1

    your expression reduces to 1 / [(u+1) u]

    use partial fraction to break it into 1/u - 1/(u+1)

    = 1/u - (u+1)^(-1)

    apply binomial series for the second term
    and change back to u = z-1
    it will be valid in |u| <1 or 0 < |z-1| < 1

    the residue at z=1 will be the coefficient of 1 / (z-1) in the series
    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, 01:46 AM
  2. Laurent Series/ Laurent Series Expansion
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 5th 2010, 09:41 PM
  3. Laurent Series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 27th 2010, 03:34 PM
  4. Laurent series
    Posted in the Calculus Forum
    Replies: 1
    Last Post: February 13th 2009, 01:10 PM
  5. Laurent Series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 17th 2007, 10:43 AM

Search Tags


/mathhelpforum @mathhelpforum