Advanced Engineering Mathematics
6th Edition
ISBN: 9781284105902
Author: Dennis G. Zill
Publisher: Jones & Bartlett Learning
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Classify the singularities for the following functions at the given point.
at a =
(a) f(z) =
1
(2 sin z-1)²
(b) f(z) =
exp(4)-1 at 0 and
at a =
(c) f(z) =
1-cosh z
at a=0
2
In the case of a pole, indicate the order of the pole and its residue.
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.
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