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Figure:
Integral contour
enclosing the upper half plane.
|
As a brief review, some definite integrals from to
can be evaluated by integrating along the contour
shown in Figure 1.
A sufficient condition on the function to be integrated, is
that
falls off at least as fast as
.
When this is the case, the integral around the outer semicircle of
is 0,
so the
.
We can evaluate the integral using residue theorem
|
(63) |
where for simple poles (single roots)
|
(64) |
and in general for a pole of order
|
(65) |
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Drexel Physics