International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 319-322
doi:10.1155/S0161171292000395

The zeros of az2J″ν(z)+bzJ′ν(z)+cJν(z) as functions of order

Abstract

If j″νk denotes the kth positive zero of the Bessel function J″ν(x), it has been shown recently by Lorch and Szego [2] that j″ν1 increases with ν in ν>0 and that (with k fixed in 2,3,…) j″νk increases in 0<ν≤3838. 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 az2J″ν(z)+bzJ′ν(z)+cJν(z). Here, the constants a, b and c are subject to certain mild restrictions.