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On the localization and computation of zeros of Bessel functions. (English) Zbl 0915.33001
In this interesting paper, an efficient method for locating , isolating and computing real zeros of Bessel functions is developed. The algorithm degree-isolate is developed to calculate the total number of real roots of Bessel functions within a pre-determined interval as also to isolate one of them. This procedure can be repeated for the isolation of each one of the zeros in this interval . Once a zero is isolated, the algorithm compute-zero is developed to compute it to any accuracy. Also, for any given interval $\left({a}_{k},{b}_{k}\right)$ containing a single zero of a Bessel function, lower and upper bounds for this zero can be determined. The number of zeros of Bessel functions of various orders $\nu$ existing within some given interval $\left(a,b\right)$, as well as the respective sub-intervals $\left({a}_{k},{b}_{k}\right)$, where exactly one root exists are presented here. Also, ten zeros of several Bessel functions, chosen at random, are given.
##### MSC:
 33C10 Bessel and Airy functions, cylinder functions, ${}_{0}{F}_{1}$ 65D20 Computation of special functions, construction of tables 34B30 Special ODE (Mathieu, Hill, Bessel, etc.)