Question: (a) Write down the explicit formulas for the harmonic polynomials of degree 4 and check that they are indeed solutions to the Laplace equation. (b)

(a) Write down the explicit formulas for the harmonic polynomials of degree 4 and check that they are indeed solutions to the Laplace equation.
(b) Prove that every homogeneous polynomial solution of degree 4 is a linear combination of the two basic harmonic polynomials.

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a x 4 6x 2 y 2 y 4 4x 3 y 4xy 3 b The polynomial ux y ax 4 bx 3 y cx 2 y ... View full answer

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