et f(z) be holomorphic on C (entire function). (a) Show that for any a, b e C, there exists R> 0 such that f(a) f(b): = a-b 2ni f(z) (z-a)(z- b) Jy dz, where y is C(0, R) oriented positively. b) If f(z) is bounded, prove that (actually) f(z) is constant.
et f(z) be holomorphic on C (entire function). (a) Show that for any a, b e C, there exists R> 0 such that f(a) f(b): = a-b 2ni f(z) (z-a)(z- b) Jy dz, where y is C(0, R) oriented positively. b) If f(z) is bounded, prove that (actually) f(z) is constant.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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please answer b using louville’s theorem
Transcribed Image Text:Let f(z) be holomorphic on C (entire function).
(a) Show that for any a, b e C, there exists R> 0 such that
f(a) f(b)
=
a-b
f(z)
$.00
2πί (z-a)(z-b)
dz,
where y is C(0, R) oriented positively.
(b) If f(z) is bounded, prove that (actually) f(z) is constant.
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