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I Another Integral Challenge

  1. Apr 21, 2016 #1

    strangerep

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    I'm up against this Laplace transform integral:
    $$F(s) ~:=~ \int^\infty_0 \exp\left( -sx + \frac{i\omega}{1+\lambda x} \right) \, dx $$where ##s## is complex, ##\omega## is a real constant, and ##\lambda## is a positive real constant.

    By inspection, I think it should converge, at least for some (nontrivial) domain of values for ##s## and ##\omega## (tell me if I'm wrong). But every symbolic integrator I've tried barfs on it.

    I figured I should at least ask here before I give up. :oldfrown:
     
  2. jcsd
  3. Apr 22, 2016 #2

    mathman

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    The only condition you need is the real part of s is > 0.
     
  4. Apr 22, 2016 #3

    strangerep

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    Yes -- I should have noted that in my opening post.

    Even so, I still don't know how to perform the integral (other than numerically -- but I want a closed form symbolic expression). :oldfrown:
     
  5. Apr 23, 2016 #4

    mathman

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