Show that J² वर J² 2 JzJZ ১৯2 ye Deduce the following for a smooth complex - valued function h. a) h is harmonic if and only if sh= = 0. b.Jh is harmonic if and only if th is analytic. JZ ch is harmonic if and only if sh is conjugate -analytic. d. If h is harmonic, hen d linen combination of JZ 4th onder partial derivative of his any jmb dzm and Jmh? Jzm

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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Show that
J²
वर
J²
2
JzJZ
১৯2 ye
Deduce the following for a smooth complex - valued function h.
a) h is harmonic if and only if sh= = 0.
b.Jh is harmonic if and only if th is analytic.
JZ
ch is harmonic if and only if sh is conjugate -analytic.
d. If h is harmonic, hen
d
linen combination of
JZ
4th onder partial derivative of his
any jmb
dzm
and Jmh?
Jzm
Transcribed Image Text:Show that J² वर J² 2 JzJZ ১৯2 ye Deduce the following for a smooth complex - valued function h. a) h is harmonic if and only if sh= = 0. b.Jh is harmonic if and only if th is analytic. JZ ch is harmonic if and only if sh is conjugate -analytic. d. If h is harmonic, hen d linen combination of JZ 4th onder partial derivative of his any jmb dzm and Jmh? Jzm
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