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hw10_2 - z = ∞ X n =0 z 2 n 1(2 n 1 for all z ∈ C...

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Complex Variables Assignment 10.2 Spring 2011 Due November 7 Exercise 1. What is the largest circle within which the Taylor series at z 0 = 0 for the function tanh z converges to tanh z ? Find the first two nonzero terms of this series. Exercise 2. Prove that sinh
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Unformatted text preview: z = ∞ X n =0 z 2 n +1 (2 n + 1)! for all z ∈ C . Exercise 3. Determine the orders of all of the zeros of f ( z ) = z sin( z 2 ). Exercise 4. What is the order of the zero of f ( z ) = e z 3-1-z 3 at the origin?...
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