Question: Suppose that a function f is analytic inside and on a positively oriented simple closed contour C and that it has no zeros on C.

Suppose that a function f is analytic inside and on a positively oriented simple closed contour C and that it has no zeros on C. Show that if f has n zeros zk (k = 1, 2, . . . , n) inside C, where each zk is of multiplicity mk, then

[Compare with equation (8), Sec. 86, when P = 0 there.]

c f(z)

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