Concerning the Roots of Jn′(x)Nn′(kx)−Jn′(kx)Nn′(x)=0
- 1 July 1943
- journal article
- Published by AIP Publishing in Journal of Applied Physics
- Vol. 14 (7) , 350-352
- https://doi.org/10.1063/1.1714997
Abstract
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.This publication has 1 reference indexed in Scilit:
- On the Roots of the Bessel and Certain Related FunctionsAnnals of Mathematics, 1894