1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Evaluating this integral (Principal value)

  1. Oct 27, 2006 #1
    Let's suppose we wish to calculate:

    [tex] PV \int_{0}^{\infty}dx\frac{e^{-sx}}{1-x} [/tex] (1)

    I don't know how to do it, my idea is take the identity:

    [tex] \frac{1}{1-x}=1+x+x^{2}+x^{3}+............ |x|<1 [/tex]

    [tex] \frac{1}{1-x}=-x^{-1}-x^{-2}-x^{-3}+x^{3}+............ |x|>1 [/tex]

    So (1) using Cauchy's principal value, is the same as to calculate with a positive small epsilon:

    [tex] \int_{0}^{1-\epsilon}dxx^{k} e^{-sx} [/tex]

    [tex] \int_{1+\epsilon}^{\infty}dxx^{-k} e^{-sx} [/tex]

    and calculate term by term integration to get the Principal value of (1)
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted

Similar Discussions: Evaluating this integral (Principal value)
  1. Evaluate this integral (Replies: 4)

  2. Cauchy Principal Value (Replies: 5)

  3. Cauchy principal value (Replies: 5)

  4. Cauchy Principal Value (Replies: 7)