4. Show thatმ2 მ2+მ2 მy2=4.მ2อะอะDeduce the following, for a smooth complex-valued function h(a) h is harmonic if and only if a2h/azz = 0.(b) h is harmonic if and only if Əh/Oz is analytic.(c) h is harmonic if and only if ah/az is conjugate-analytic 4. Show thatმ2 მ2+მ2 მy2=4.მ2อะอะDeduce the following, for a smooth complex-valued function h(a) h is harmonic if and only if a2h/azz = 0.(b) h is harmonic if and only if Əh/Oz is analytic.(c) h is harmonic if and only if ah/az is conjugate-analytic

EXPLANATION: For the problems (a) to (d), use the foundational concepts from complex…

Answered: 4. Show that მ2 მ2 + მ2 მy2 = 4. მ2…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 50E

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Question

4. Show that
მ2 მ2
+
მ2 მy2
=
4.
მ2
อะอะ
Deduce the following, for a smooth complex-valued function h
(a) h is harmonic if and only if a2h/azz = 0.
(b) h is harmonic if and only if Əh/Oz is analytic.
(c) h is harmonic if and only if ah/az is conjugate-analytic

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