Bounds for the small real and purely imaginary zeros of Bessel and related functions

@inproceedings{Ismail1995BoundsFT,
  title={Bounds for the small real and purely imaginary zeros of Bessel and related functions},
  author={Mourad E. H. Ismail and Martin E. Muldoon},
  year={1995}
}
We give two distinct approaches to finding bounds, as functions of the order ν, for the smallest real or purely imaginary zero of Bessel and some related functions. One approach is based on an old method due to Euler, Rayleigh, and others for evaluating the real zeros of the Bessel function Jν(x) when ν > −1. Here, among other things, we extend this method to get bounds for the two purely imaginary zeros which arise in the case −2 < ν < −1. If we use the notation jν1 for the smallest positive… CONTINUE READING