Scries. 7(10p). Prove the Argument Principle: If f is meromorphic on a domain D with smooth boundary and f is analytic and non-vanishing on OD, then 1 2πί f'(z) aD f(z) dz = No - Noo, where No and No stand for the number of zeros and poles of f, respectively, counting multiplicity.

Scries. 7(10p). Prove the Argument Principle: If f is meromorphic on a domain D with smooth boundary and f is analytic and non-vanishing on OD, then 1 2πί f'(z) aD f(z) dz = No - Noo, where No and No stand for the number of zeros and poles of f, respectively, counting multiplicity.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter11: Topics From Analytic Geometry

Section11.4: Plane Curves And Parametric Equations

Problem 34E

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Question

Scries.
7(10p). Prove the Argument Principle: If f is meromorphic on a domain D with smooth
boundary and f is analytic and non-vanishing on OD, then
1
2πί
f'(z)
aD f(z)
dz = No - Noo,
where No and No stand for the number of zeros and poles of f, respectively, counting
multiplicity.

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