Another Integral Challenge

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  • Thread starter strangerep
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  • #1
strangerep
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Main Question or Discussion Point

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:
 

Answers and Replies

  • #2
mathman
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The only condition you need is the real part of s is > 0.
 
  • #3
strangerep
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The only condition you need is the real part of s is > 0.
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:
 
  • #4
mathman
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