Results 1 to 3 of 3

Math Help - Complex Analysis: Laurent series

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    9

    Complex Analysis: Laurent series

    Hello,

    I m stuck with the following exercise:

    Find the Laurent series expansion about the origin of the following function:

    f(z)= cos z/ z^4

    What type of singularity does this function has at the origin?

    I can't find the laurent series.. I need help.

    Thank you in advance.

    Richard
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Nov 2009
    Posts
    1
    Just take the Taylor series of cos z and divide by z^4.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    9
    Okay I was not sure..

    So it's f(z)=1/z^4 -1/2!z^2 + 1/4! ....??

    And what about the fact that f is analytic on the punctured disc D={z \in C : 0<|z|< ? }
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Laurent series (Complex)
    Posted in the Differential Geometry Forum
    Replies: 9
    Last Post: May 15th 2010, 01:03 AM
  2. Complex Analysis: Laurent Series
    Posted in the Calculus Forum
    Replies: 7
    Last Post: December 8th 2008, 04:19 PM
  3. Complex Analysis - Cauchy Riemann Equations + Laurent Expansions
    Posted in the Differential Equations Forum
    Replies: 6
    Last Post: August 5th 2008, 10:24 AM
  4. complex analysis: Laurent series
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 20th 2007, 12:15 PM
  5. Laurent Series-Complex
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 20th 2006, 06:54 AM

Search Tags


/mathhelpforum @mathhelpforum