Statement
Suppose
is a function (possibly with isolated singularities) on an open subset
of
, that contains the real axis and upper half-plane
, such that
has no essential singularities in the strict upper half-plane, and only finitely many poles on the real axis and in the upper half-plane. Suppose further that:
Then, if
denotes the semicircle of radius
centered at the origin, and if
, we have:
Thus, we get:
where the sum is taken over all poles in the upper half-plane.