Advanced Engineering Mathematics
Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Determine all functions f analytic in the open unit disc || < 1 which satisfy in addition f(0) = 1 and |f(z)|≥ 1 whenever || < 1. Justify your answer.
Deduce the Laurent expansion for f(z) = 22(2-3)2 in the annulus 0 < |z3|< 3.
What can you conclude about a complex-valued function f(z) that satisfies 1. f is complex differentiable everywhere 2. ƒ(z+1) = ƒ(z) for all z 3. For a fixed complex number a with nonzero imaginary part, f(z+a) = f(z) for all z ? Justify your answer. (Hint: Use Liouville's theorem.)
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