Results 1 to 3 of 3

Math Help - contour integral with singularities on the contour

  1. #1
    Newbie
    Joined
    Nov 2012
    From
    italy
    Posts
    9

    contour integral with singularities on the contour

    I want to compute the following integral
    \oint_{|z|=1}\frac{\exp(\frac{1}{z})}{z^2-1}\,dz
    The integrand has essential singularity at the origin, and 2-poles at \pm 1,which lie on the curve |z|=1 so i can't apply residue formula. How can i proceed?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Sep 2012
    From
    Planet Earth
    Posts
    215
    Thanks
    56

    Re: contour integral with singularities on the contour

    Ive never seen integration where the singularities lie on the contour, is that even defined?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2012
    From
    NY
    Posts
    62
    Thanks
    8

    Re: contour integral with singularities on the contour

    You need to define the contour with small semi-circles around the poles of radius some \delta and then take the limit as \delta tends to zero. In that way the function will be analytic in the domain that has avoided the singularities. When f is analytic inside a domain D the integral over D of f = 0. Check any book on complex analysis. You can find the details.
    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, 11:00 PM
  2. [SOLVED] Though contour integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 6th 2010, 08:54 AM
  3. Contour Integral
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: December 7th 2009, 01:37 PM
  4. Dumbbell Contour Integral
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: October 31st 2009, 10:13 AM
  5. contour integral-need help
    Posted in the Advanced Math Topics Forum
    Replies: 2
    Last Post: October 27th 2009, 10:48 AM

Search Tags


/mathhelpforum @mathhelpforum