- #1
Niles
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Homework Statement
Hi all.
I have the following integral:
[tex]
I = \int_{2 - i\infty}^{2+i\infty}{f(s) \exp(st)ds},
[/tex]
where [itex]f(s)[/itex] is some function. In order to perform this integral, I will choose to close the vertical line with a semi-circle in some halfplane (in order to use Cauchy's integral theorem), but this requires that the contribution from the semi-circle is zero.
Question: Now, let us say that for the specific [itex]f(s)[/itex] in this case, then the contribution from the semi-circle in e.g. the right halfplane does go to zero: With this in mind, then will the limit [itex]f(s)\exp(st)[/itex] for [itex]s\rightarrow \infty[/itex] be zero?Thank you very much in advance.Niles.
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