TEAM PROJECT. Zeros. la) Derivative. Show that if f(:) has a zero of order 11 > I at: =
Chapter 16, Problem 16.1.49(choose chapter or problem)
Zeros.
(a) Derivative. Show that if f(z) has a zero of order n > 1 at \(z={z}_{0}\). then f ‘ (z) has a zero of order n - 1 at \(z_{0}\).
(b) Poles and zeros. Prove Theorem 4.
(c) Isolated k - points. Show that the points at which a nonconstant analytic function f(z) has a given value k are isolated.
(d) Identical functions. If \(f_{1}(z)\) are analytic in a domain D and equal at a sequence of points \(z_{n}\) in D that converges in D, show that \(f_{1}(z) \equiv f_{2}(z)\) in D.
Text Transcription:
z = z_0
z_0
f_1(z)
z_n
f_1(z) equiv f_{2}(z)
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