Results 1 to 2 of 2

Math Help - Complex Contour Integral

  1. #1
    Member
    Joined
    Aug 2008
    Posts
    88

    Complex Contour Integral

    Let C be any simple closed contour described in the positive sense. Given g(z)=\int_{C} \frac{s^3+2s}{(s-z)^3}ds, a)show that g(z)=6 \pi iz when z is inside C and b)show that g(z)=0 when z is outside.

    Part a) was easy, but I don't see how to start part b). The Cauchy integral formula has the requirement that the point of interest be interior to C, so how else could I go about showing g(z)=0 for an arbitrary simple closed contour when the point is exterior to C?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by davesface View Post
    Let C be any simple closed contour described in the positive sense. Given g(z)=\int_{C} \frac{s^3+2s}{(s-z)^3}ds, a)show that g(z)=6 \pi iz when z is inside C and b)show that g(z)=0 when z is outside.

    Part a) was easy, but I don't see how to start part b). The Cauchy integral formula has the requirement that the point of interest be interior to C, so how else could I go about showing g(z)=0 for an arbitrary simple closed contour when the point is exterior to C?
    Read this: The Cauchy-Goursat Theorem
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contour integral, limiting contour theorem with residue
    Posted in the Differential Geometry Forum
    Replies: 6
    Last Post: May 23rd 2011, 10:00 PM
  2. Complex Contour Integrals
    Posted in the Calculus Forum
    Replies: 6
    Last Post: October 16th 2010, 09:50 PM
  3. Complex Contour Integral
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 23rd 2010, 11:58 AM
  4. Complex contour integration
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: April 3rd 2010, 05:21 PM
  5. Complex Contour Question
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 25th 2009, 04:00 PM

Search Tags


/mathhelpforum @mathhelpforum