Assume that f .x; y/ is harmonic in the xy-plane. Show that
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Assume that f .x; y/ is harmonic in the xy-plane. Show that each of the functions z f .x; y/, x f .y; z/, and y f .z; x/
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Assume that f .x; y/ is harmonic in the xy-plane. Show that each of the functions z f .x; y/, x f .y; z/, and y f .z; x/ is harmonic in the whole of R3 . What condition should the constants a, b, and c satisfy to ensure that f .ax C by; cz/ is harmonic in R3 ?
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