Differential inequalities for the positive zeros of Bessel functions

摘要

Let jv,k be the kth positive zero of the Bessel function Jv(z) of the first kind and order v > −1. We prove the differential inequalities where hn,v(x), n ⩾ 0, are the Lommel polynomials (Watson, 1966). As a consequence we obtain some new lower and upper bounds for jv,k improving previously known results.