A differential inequality for the positive zeros of Bessel functions

AbstractIt is proved that the positive zeros jν, k, k = 1,2,…, of the Bessel function Jν(x) of the first kind and order ν > − 1, satisfy the differential inequality jν, k, djν, kdν > 1 + (1 + j2ν, k)12, ν > − 1. This inequality improves the well-known inequality djν, kdν > 1, ν > − 1, which is the source of a large number of lower and upper bounds for the zeros jν, k, k = 1, 2,…