International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 319-322
The zeros of as functions of order
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 denotes the positive zero of the Bessel function , it has been shown recently by Lorch and Szego  that increases with in and that (with fixed in ) increases in . Furthermore, Wong and Lang have now extended the latter result, as well, to the range . 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 . Here, the constants , and are subject to certain mild restrictions.