The zeros of a z 2 J ″ ν ( z ) + b z J ′ ν ( z ) + c J ν ( z ) as functions of order

A. McD. Mercer

International Journal of Mathematics and Mathematical Sciences, 1992, vol. 15, 1-4

Abstract:

If j ″ ν k denotes the k t h positive zero of the Bessel function J ″ ν ( x ) , it has been shown recently by Lorch and Szego [2] that j ″ ν 1 increases with ν in ν > 0 and that (with k fixed in 2 , 3 , … ) j ″ ν k 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 a z 2 J ″ ν ( z ) + b z J ′ ν ( z ) + c J ν ( z ) . Here, the constants a , b and c are subject to certain mild restrictions.

Date: 1992
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:814850

DOI: 10.1155/S0161171292000395

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