ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument

A reliable and portable software package, called ZEBEC (ZEros of BEssel functions Complex), is presented, which localizes and computes simple zeros of Bessel functions of the first, the second or the third kind, or their derivatives. The Bessel functions are of real order and complex argument. ZEBEC calculates with certainty the total number of zeros within a given box whose edges are parallel to the coordinate axes. Cauchy's Theorem is used for this calculation. Then the program isolates each one of the zeros, utilizing the above-mentioned theorem, and finally computes them to a given desired accuracy using a generalized method of bisection.