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How to determine where $$f(z)=\int_0^\infty \frac{e^{tz}}{1+t^2} \, dt$$ is defined and holomorphic using Morera's and Fubini's theorem?

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    So, what would you need to do to apply Morera's theorem to show that $f(z)$ is analytic in a region $G$?2012-09-24
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    @MhenniBenghorbal: what happens if limits of integration is from -1 to 1?2012-09-24
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    @abby:The integral has no problem at these points. See the answer.2012-09-24

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