THE ZEROS OF az J(z)+ bzJ;(z)+ cJv(z) AS FUNCTIONS OF ORDER

ABSTRACT If denotes the kth positive zero of the Bessel function J(x), it has been shown.lvk recently by Lorch and Szego [2] that Jl increases with v in v) 0 and that (with k fixed in 2,3,...) j " increases in 0 (v < 3838. Furthermore, Wong and Lang have now extended the latter result, s well, to the range v)0. The present paper, by using a different kind of anMysis, re-obtains these conclusions &s a speciM case of a more general result concerning the positive zeros of the function 2az Jr(z)+bzJ(z)+ cJv(z). Here, the constants a,b md e are subject to certain mild restrictions