z=x+iy, consider the entire function f(z)=u(x,y) + iv(x,y) where u(x,y)=3x2y+2x2-y3-2y2. Prove that u is harmonic. Find the harmonic conjugate v of u so that f=u+iv is holomorphic

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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if z=x+iy, consider the entire function f(z)=u(x,y) + iv(x,y) where u(x,y)=3x2y+2x2-y3-2y2.

Prove that u is harmonic.

Find the harmonic conjugate v of u so that f=u+iv is holomorphic

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