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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 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

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 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

Algebra & Trigonometry with Analytic Geometry
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
Transcribed Image Text: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
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
Transcribed Image Text: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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