Elementary approximations for zeros of Bessel functions

AbstractLet jvk, yvk and cvk denote the kth positive zeros of the Bessel functions Jv(x), Yv(x) and of the general cylinder function Cv(x) = cos αJv(x)−sin αYv(x), 0 ⩽ α < π, respectively. In this paper we extend to cvk, k = 2, 3,..., some linear inequalities presently known only for jvk. In the case of the zeros yvk we are able to extend these inequalities also to k = 1. Finally in the case of the first positive zero jv1 we compare the linear enequalities given in [9] with some other known inequalities