I seem to be missing a subtlety of the definition of a harmonic function. I'm using Churchill and Brown. As stated in the book, an analytic function in domain D with component functions (i.e. real and imaginary parts) u(x,y) and v(x,y) are harmonic in D.(adsbygoogle = window.adsbygoogle || []).push({});

harmonic functions satisfy u_{xx}+u_{yy}=0

Consider u=x^{3}+y

then u_{xx}+u_{yy}gives 6x+0 [tex]\neq[/tex] 0

but this is analytic in some domain D.

So what am I missing here, why does this not satisfy the conditions to be a harmonic function?

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# Complex analysis harmonic function

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