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Theorem 1 (For open convex domain). Suppose 2 is a convex open set. Let f be analytic in 2 \{a} and continuous on 2. Then, = 0, (4.20) where y is a simple closed contour contained in the domain.

Theorem 1 (For open convex domain). Suppose 2 is a convex open set. Let f be analytic in 2 \{a} and continuous on 2. Then, = 0, (4.20) where y is a simple closed contour contained in the domain.

Advanced Engineering Mathematics
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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Let f be analytic in 2\{a, a2,. , an} and continuous on 2, where 2 is open a convex. Let p and q be any two points in 2 and let y be any contour joining thes points. Then show that .... S(2) dz = f(2) dz. (pg) TI 10 a ompie GIUSEU CUnour containea in the domain. 8. Let D be star-shaped at a, and f be analytic in D. Then there exists an analytic function F(z) in D such that F'(z) = fiz) in D. In particular, (4.20) holds. 4.20 is as follows Theorem 1 (For open convex domain). Suppose is a convex open set. Let f be analytic in 2 \{a} and continuous on 2. Then, Srapiz = 0, (4.20) where y is a simple closed contour contained in the domain.
Transcribed Image Text:Let f be analytic in 2\{a, a2,. , an} and continuous on 2, where 2 is open a convex. Let p and q be any two points in 2 and let y be any contour joining thes points. Then show that .... S(2) dz = f(2) dz. (pg) TI 10 a ompie GIUSEU CUnour containea in the domain. 8. Let D be star-shaped at a, and f be analytic in D. Then there exists an analytic function F(z) in D such that F'(z) = fiz) in D. In particular, (4.20) holds. 4.20 is as follows Theorem 1 (For open convex domain). Suppose is a convex open set. Let f be analytic in 2 \{a} and continuous on 2. Then, Srapiz = 0, (4.20) where y is a simple closed contour contained in the domain.
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