Results 1 to 1 of 1

Thread: sum, zeros, poles

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    16

    sum, zeros, poles

    Let $\displaystyle f(z)=\frac{p(z)}{q(z)}$, where $\displaystyle p(z)$ and $\displaystyle q(z)$ are polynomials. Prove that the sum of multiplicities of all zeroes minus the sum of orders of all poles, including zeroes or poles at $\displaystyle \infty$, equals zero.


    I am not sure how to prove this. I was thinking to use the argument principle somehow. However, could not figure out how. I need some hints on how this one. Thanks.
    Last edited by xboxlive89128; Feb 19th 2010 at 03:36 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. meromorphic map and poles
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: Apr 23rd 2011, 04:11 AM
  2. power of poles
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Jul 13th 2010, 08:36 AM
  3. zeros and poles
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Oct 10th 2009, 05:03 AM
  4. poles
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Nov 9th 2008, 03:55 PM
  5. Poles
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Aug 27th 2008, 02:01 AM

Search Tags


/mathhelpforum @mathhelpforum