Uniform upper and lower bounds on the zeros of Bessel functions of the first kind (Q1910042)

The author derives upper and lower bounds for the positive zeros \(j_{\nu,k}\), \(k = 1,2, \dots\), of the Bessel function \(J_\nu (x)\) in terms of the zeros \(a_k\), \(k = 1, 2, \dots\), of the Airy function \(Ai (x)\). These bounds hold, except for one lower bound, for all real \(\nu \geq 1/2\) and are close to asymptotic approximations which instead are valid only when \(k\) or \(\nu\) are very large.