Bounds on differences of adjacent zeros of Bessel functions and iterative relations between consecutive zeros (Q2719074)

Real zeros are considered of the cylinder functions \(C_\nu(x)=\cos\alpha J_\nu(x)-\sin \alpha Y_\nu(x)\), \(\alpha\in[0,\pi)\), \(\nu\) real. In particular bounds on the difference of adjacent zeros are given. These bounds, together with the application of Newton methods based on the monotonicity of certain auxiliary functions, yield forward and backward iterative relations between consecutive zeros of the cylinder functions. Numerical examples illustrate the methods to find all positive zeros of \(C_\nu(x)\) inside given real intervals.