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Concerning the Roots of Jn′(x)Nn′(kx)-Jn′(kx)Nn′(x)=0

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1 Author(s)
Truell, Rohn ; RCA Laboratories, Princeton, New Jersey

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The relation Jn′(x)Nn′(kx)-Jn′(kx)Nn′(x)=0 arises in certain resonant cavity problems having cylindrical symmetry. The first roots of this relation are presented here as a function of k for n = 1, 2, 3, 4. The M'Mahon relation does not allow calculation of the first roots despite statements to the contrary in several places. It is shown that the functions Jn′(x)/Nn′(x) have relative maxima at x = n except for n = 0.

Published in:

Journal of Applied Physics  (Volume:14 ,  Issue: 7 )