Problem 7: In each part determine the type of singularity of f(z) at zo (removable, essential or a ole) and find the residue of f(z) at zo. If f(z) has a pole at zo, determine the order of this pole. (a) f(2)= - 2²+1 at 20 = 0, at zo= 0, (b) f(2)= - 3 cos(z) 2z - T at zo = π 2 (c) f(z) = (e¹/² - 1)² at zo = 0.
Problem 7: In each part determine the type of singularity of f(z) at zo (removable, essential or a ole) and find the residue of f(z) at zo. If f(z) has a pole at zo, determine the order of this pole. (a) f(2)= - 2²+1 at 20 = 0, at zo= 0, (b) f(2)= - 3 cos(z) 2z - T at zo = π 2 (c) f(z) = (e¹/² - 1)² at zo = 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Problem 7: In each part determine the type of singularity of f(z) at zo (removable, essential or a
pole) and find the residue of ƒ(z) at zo. If ƒ(z) has a pole at zo, determine the order of this pole.
cos(z)
2² +1
(a) f(z) =
23
(c) ƒ(z) = (e¹/² − 1)² at zo = 0.
2z - π
at zo = 0, (b) ƒ(z) :
=
at zo
=
ㅠ
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