APM346-2015F > Final Exam

FE-7

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Victor Ivrii:
\begin{equation*}
u=\underbracket{\frac{3}{5}zx^2+\frac{3}{5}zy^2-\frac{2}{5}z^3}+\underbracket{\frac{2}{5}z}
\end{equation*}
only 2 homogeneous harmonic polynomials as in your decomposition two have the same order of homogeneity and count as one (as they could be joined)

Those who did not use "rotational symmetry and odd with respect to $z$" arguments were forced to use $u=z (x^2+y^2) - (Ax+By+Cz +D) (x^2+y^2+z^2-1)$ rather than $u=z (x^2+y^2) - Cz (x^2+y^2+z^2-1)$ and never performed calculations.

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