The zeros of az2J ￠ € 3 (z)+bzJ ￠ € 2 (z)+cJ (z) as functions of order

If j ￠ € 3 k denotes the kth positive zero of the Bessel function J ￠ € 3 (x), it has been shown recently by Lorch and Szego [2] that j ￠ € 3 1 increases with in >0 and that (with k fixed in 2,3, ￠ € |) j ￠ € 3 k increases in 0< ￠ ‰ ¤3838. 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 ￠ € 3 (z)+bzJ ￠ € 2 (z)+cJ (z). Here, the constants a, b and c are subject to certain mild restrictions.