Monotonicity and concavity properties of zeros of Bessel functions

AbstractLet jνk, yνk and cνk denote the kth positive zeros of the Bessel functions Jν(x), Yν(x) and of the general cylinder function Cν(x), respectively. We show, among other things, that, for k = 2, 3,… and 0 < ν < ∞, cνk is a concave function of ν, cνk > ν + c0k and cνk[v + (2π)c0k] decreases as ν increases. In the cases of jνk and yνk, these results hold also for k = 1