International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 319-322

The zeros of az2Jν(z)+bzJν(z)+cJν(z) as functions of order

A. McD. Mercer

Department of Mathematics and Statistics, University of Guelph, Ontario, N1G 2W1, Canada

Received 2 July 1991; Revised 3 October 1991

Copyright © 1992 A. McD. Mercer. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


If jνk denotes the kth positive zero of the Bessel function Jν(x), it has been shown recently by Lorch and Szego [2] that jν1 increases with ν in ν>0 and that (with k fixed in 2,3,) jνk increases in 0<ν3838. Furthermore, Wong and Lang have now extended the latter result, as well, to the range ν>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 az2Jν(z)+bzJν(z)+cJν(z). Here, the constants a, b and c are subject to certain mild restrictions.