Error bounds for a uniform asymptotic approximation of the zeros of the Bessel function Jν(x)

A recent asymptotic expansion for the positive zeros [Formula: see text] ([Formula: see text]) of the Bessel function of the first kind [Formula: see text] is studied, where the order [Formula: see text] is positive. Unlike previous well-known expansions in the literature, this is uniformly valid for one or both [Formula: see text] and [Formula: see text] unbounded, namely [Formula: see text] and [Formula: see text]. Explicit and simple lower and upper error bounds are derived for the difference between [Formula: see text] and the first three terms of the expansion. The bounds are sharp in the sense they are close to the value of the fourth term of the expansion (i.e. the first neglected term).