Express your answer in terms of trigonometric functions (of πz).
2.
Let C be a simple closed contour and Ci be the interior of C.
Suppose that f(z) is analytic and nonzero on C, meromorphic in Ci, and
that in Ci, f has zeroes at a1, ..., aN, and poles at
b1, …, bM. Let H(z) be analytic on C and Ci.
Then
\frac12πi
⌠ (⎜) ⌡
C
H(z)\fracf′(z)f(z) dz =
N ∑ j=1
H(aj) −
M ∑ k=1
H(bk),
where each zero and pole occurs as often in the sum as is
required by its multiplicity.
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