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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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I need help with attached complex analysis question. We are in Cauchy
Transcribed Image Text:3. Evaluate the following integral
eiz
-dz
z(z – 1)
-
C
for each of the following four cases (all circles are centered at the origin. Use Eq. (1.2.19) as
necessary).
(-1)İz²j+1
2j=0 (2j+1)!
(-1)İz²j
(2j)!
ez = Lj=0°
100
100
sin z =
cos z = 2j=0
j!
z²j+1
sinh z = Lj=0(2j+1)!
z²j
cosh z = Lj=0 (2j)!
00
(1.2.19)
(a) C is the boundary of the annulus between circles of radius 1 and radius 3.
(b) C is the boundary of the annulus between circles of radius 1 and radius 4.
(c) C is a circle of radius R, where R > T.
(d) C is a circle of radius R, where R < T.
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