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(a) Mean value property show that the value of a harmonic function Ф at the center of a circle equals the mean of the value of Ф on C (See Sec, 18.4, footnote 1, for definitions of mean values).
(b) Separation of variables, Show that the terms of (7) appear as solutions in separating the Laplace equation in polar coordinates.
(c) Harmonic conjugate, find a series for a harmonic conjugate ψ of Ф from (7).
(d) Power series, find a series for F(z) = Ф + iψ. |
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