%0 Journal Article
%T The zeros of az2J ¡é ? 3    (z)+bzJ ¡é ? 2    (z)+cJ    (z) as functions of order
%A A. McD. Mercer
%J International Journal of Mathematics and Mathematical Sciences
%D 1992
%I Hindawi Publishing Corporation
%R 10.1155/s0161171292000395
%X If j ¡é ? 3    k denotes the kth positive zero of the Bessel function J ¡é ? 3    (x), it has been shown recently by Lorch and Szego [2] that j ¡é ? 3    1 increases with      in     >0 and that (with k fixed in 2,3, ¡é ? |) j ¡é ? 3    k increases in 0<     ¡é ¡ë ¡è3838. Furthermore, Wong and Lang have now extended the latter result, as well, to the range     >0. The present paper, by using a different kind of analysis, re-obtains these conclusions as a special case of a more general result concerning the positive zeros of the function az2J ¡é ? 3    (z)+bzJ ¡é ? 2    (z)+cJ    (z). Here, the constants a, b and c are subject to certain mild restrictions.
%K Bessel functions
%K zeros
%K eigenvalues
%K boundary-value problems
%K ordinary differential equations.
%U http://dx.doi.org/10.1155/S0161171292000395