On the zeros of J_n(z) ± iJ_(n+1)(z) and [J_(n+1)(z)]~2 - J_n(z)J_(n+2)(z)

摘要

The zeros of J_n(z) ± iJ_(n+1)(z) and [J_(n+1)(z)]~2 - J_n(z)J_(n-2)(z) play an important role in certain physical applications. At the origin these functions have a zero of multiplicity n (if n ≥ 1) and 2n + 2, respectively. We prove that all the zeros that lie in C_0 simple. ZEBEC (Kravanja et al., Comput. Phys. Commun. 113(2-3) (1998) 220-238) is a reliable software package for calculating zeros of Bessel functions of the first, the second, or the third kind, or their first derivatives. It can be easily extended to calculate zeros of any analytic function, provided that the zeros are known to be simple. Thus ZEBEC is the package of choice to calculate the zeros of J_n(z) ± iJ_(n+1)(z) or [J_(n+1)(z)]~2 - J_n(z)J_(n+2)(z). We tabulate the first 30 zeros of J_5(z) - iJ_6(z) and J_(10)(z) - iJ_(11)(z) that lie in the fourth quadrant as computed by ZEBEC.