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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

international journal of mathematics and mathematical sciences

The zeros of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="$az^2 J''_\nu \left( z \right) + bzJ'_\nu \left( z \right) + cJ_\nu \left( z \right)$"><mml:mrow><mml:mi>a</mml:mi><mml:msup><mml:mi>z</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:msub><mml:msup><mml:mi>J</mml:mi><mml:mo>″</mml:mo></mml:msup><mml:mi>ν</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>z</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:mi>b</mml:mi><mml:mi>z</mml:mi><mml:msub><mml:msup><mml…

The zeros ofaz2J″ν(z)+bz