The zeros of <mml:math alttext="$az^2 J''_\nu \left( z \right)

Ifj″νkdenotes thekthpositive zero of the Bessel functionJ″ν(x), it has been shown recently by Lorch and Szego [2] thatj″ν1increases withνinν>0and that (withkfixed in2,3,…)j″νkincreases in0<ν≤3838. Furthermore, Wong and Lang have now extended the latter result, as well, to the rangeν>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 functionaz2J″ν(z)+bzJ′ν(z)+cJν(z). Here, the constantsa,bandcare subject to certain mild restrictions.