Electromagnetic Theory volume 2

Cover Electromagnetic Theory volume 2
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Ull. Vlt.
Comparing with (140) we see that Here we have an identity of the original kind, a power series expanded in I functions. Its truth may be now verified by the same formula (63) from which we started, or, more easily, by (68).
But (147) by itself is of no use. The terms omitted from (140) are vital in the electromagnetic wave problem we started with. Equation (147) may, of course, be generalised to a wave, if the left side be taken to represent V eP* ; but that is another question. It is
... (142) that is the generalisation of (140), and requires development. The differentiated part is 111 C so the full wave is Vf^^iog^J+ffp. Log* e ( - 1 w v - ... , (148) -^i-ia- ..... (149) This is complete, and is finite everywhere save at the wave front. As regards the values of g'(n), they are r^z, (150) ELECTROMAGNETIC WAVES. 36 1 when n is a positive integer. Also, on the negative side, it is easier still, thus, (151) Xot being able to do everything at once, I must defer the proof of these side results.

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