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Contour integration
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====Contour note==== As an aside, a question can arise whether we do not take the semicircle to include the ''other'' singularity, enclosing {{math|β''i''}}. To have the integral along the real axis moving in the correct direction, the contour must travel clockwise, i.e., in a negative direction, reversing the sign of the integral overall. This does not affect the use of the method of residues by series.
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