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Complex Analysis

  1. May 10, 2006 #1
    I have two questions on complex integration, and I do not know how to solve them. Please help if you can.


    1. Evaluate the following principal value integral using an appropriate contour.

    Integration of (integral goes from 0 to infinity) : (x)^a-1/1-x^2,

    2.Using contour integration and calculus of residues, find the sum

    Summation (going from 0 to infinity) 1/n^2 +a^2
  2. jcsd
  3. May 11, 2006 #2


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    Homework Helper

    Hi, you'll get the most help if you provide whatever work you have, even if it doesn't appear to lead anywhere.

    1) Have you seen a similar problem, but with no pole on the path of integration?

    2) For series like this, a standard approach is to relate the sum to the poles of cot(Pi*z) multiplied by the appropriate function. Have you seen this method before and if so what happens when you try to apply it here?
  4. May 12, 2006 #3
    Show some work first.

    Here are some tips :

    1) Do you know the theorems that you need to use the appropriate contour ?

    2) This is an analytic multivalued function (because of the a exponent) so be sure to use the branch cut. Do you know about this ?

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