i. Let Cr be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) = zo + r exp(it) where r > 0. Explain why ii. Show that f(z) f(z) | 1(2), dz = √ (²) dz. 2-20 2-20 - 20 dz - 2πif (zo) = √[ƒ(²) - ƒ (20) 20 dz.
i. Let Cr be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) = zo + r exp(it) where r > 0. Explain why ii. Show that f(z) f(z) | 1(2), dz = √ (²) dz. 2-20 2-20 - 20 dz - 2πif (zo) = √[ƒ(²) - ƒ (20) 20 dz.
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. Let CÃ be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) =
zo + r exp(it) where r > 0. Explain why
ii. Show that
f(z)
C 2 - 20
So
ƒ(z)
Set
-
20
dz
f(z)
Jaz
-
dz - 2πif (zo) = Sci
Cr
20
dz.
ƒ(z) — ƒ(zo)
2- 20
dz.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0d2dbea-0987-4c02-a00c-0b87f219c8f9%2F6fc8c9a3-5090-4162-928d-24727cec0d94%2Fqfosffzi_processed.png&w=3840&q=75)
Transcribed Image Text:=
i. Let CÃ be a contour lying inside C, parametrised by y : [0, 2π] → C, y(t) =
zo + r exp(it) where r > 0. Explain why
ii. Show that
f(z)
C 2 - 20
So
ƒ(z)
Set
-
20
dz
f(z)
Jaz
-
dz - 2πif (zo) = Sci
Cr
20
dz.
ƒ(z) — ƒ(zo)
2- 20
dz.
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