Results 1 to 2 of 2

Thread: Calculating a residue

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    3

    Calculating a residue

    does anyone know how to work out the residue of this at 0

    i already have that
    Res(f,0)= .5 lim (2*pi^3*z*cot(pi*z) -2*pi^2)cosec^2(pi*z)
    (as z tends to 0)

    But i cant work out the limit, seeing as everytime i work it out i get different answers, i was told to use taylor series though
    Last edited by mr fantastic; Jan 5th 2009 at 12:27 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    10
    Quote Originally Posted by pols89 View Post
    does anyone know how to work out the residue of this at 0

    i already have that
    Res(f,0)= .5 lim (2*pi^3*z*cot(pi*z) -2*pi^2)cosec^2(pi*z)
    (as z tends to 0)
    Write cot(πz) as cos(πz)/sin(πz) and cosec(πz) as 1/sin(πz). Then you get \lim_{z\to0}\frac{\pi^2(\pi z\cos(\pi z) - \sin(\pi z))}{\sin^3(\pi z)}. Now use the power series expansions of sin and cos to find the lowest power of z with nonzero coefficient. I make the limit -\pi^2/3.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. calculating a residue
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Jun 25th 2011, 10:38 PM
  2. residue
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: May 23rd 2011, 01:17 PM
  3. residue
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Apr 27th 2011, 05:43 AM
  4. Need help calculating a Residue
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: Dec 24th 2010, 11:38 AM
  5. residue
    Posted in the Differential Geometry Forum
    Replies: 11
    Last Post: Dec 4th 2009, 06:31 AM

Search Tags


/mathhelpforum @mathhelpforum