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If the number of terms in the series is finite (say N), /(£)<-> I 0nt/n(f) (2.36) then we
can ask for the "best" choice of coefficients an so that we get the "best"
representation of the function /(f). If "best" is defined as minimizing the mean
square error ...
(3.33) on the surface of the sphere: V(0) = f Ap'Pfcos 0) (3.34) 1=0 This is just a
Legendre series of the form (3.23), so that the coefficients A, are: /1, = ^-^- K(0)P,(
cos 0) sin 0 d6 (3.35) 2a Jo If, for example, K(0) is that of Section 2.8, with two ...
The coefficients Aim in (16.35) are not completely arbitrary. The divergence
condition V • B = 0 must be satisfied. Since the radial functions are linearly
independent, the condition V • B = 0 must hold for the two sets of terms in (16.35)
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Introduction to Electrostatics
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