Let f be continuous on S(0, 1) = {z : |2| = 1}. 1. Show that f(2) -dz. f(2)dz: S(0,1) 22 Use the identity g(t)dt = S" g(t)dt which holds for any continuous function g : [a,b] → C. 2. Let f be an entire function. Prove that f(z) -dz f(0), if |a| < 1; 1 2ni S(0,1) 2 - a f(0) – f(ā-1), if Ja| > 1.
Let f be continuous on S(0, 1) = {z : |2| = 1}. 1. Show that f(2) -dz. f(2)dz: S(0,1) 22 Use the identity g(t)dt = S" g(t)dt which holds for any continuous function g : [a,b] → C. 2. Let f be an entire function. Prove that f(z) -dz f(0), if |a| < 1; 1 2ni S(0,1) 2 - a f(0) – f(ā-1), if Ja| > 1.
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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plz answer 1st question
![Let f be continuous on S(0, 1) = {z : |2| = 1}.
1. Show that
f(2)
-dz.
f(2)dz:
S(0,1)
22
Use the identity g(t)dt = S" g(t)dt which holds for any continuous function g : [a,b] → C.
2. Let f be an entire function. Prove that
f(z)
-dz
f(0),
if |a| < 1;
1
2ni
S(0,1)
2 - a
f(0) – f(ā-1),
if Ja| > 1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82cc8ab0-224e-4e63-b325-2c789c823e3d%2F3a32bbdf-704e-488a-8da2-674709e97a34%2Fwy0fpy_processed.png&w=3840&q=75)
Transcribed Image Text:Let f be continuous on S(0, 1) = {z : |2| = 1}.
1. Show that
f(2)
-dz.
f(2)dz:
S(0,1)
22
Use the identity g(t)dt = S" g(t)dt which holds for any continuous function g : [a,b] → C.
2. Let f be an entire function. Prove that
f(z)
-dz
f(0),
if |a| < 1;
1
2ni
S(0,1)
2 - a
f(0) – f(ā-1),
if Ja| > 1.
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