This paper shows the construction of an algorithm to calculate the roots of both, the cross-product of Bessel functions respectively of their first derivatives. The algorithm has shown globally convergent behavior for a large range of values of the argument and of the order of the Bessel functions with the desired accuracy to machine precision.
Nikolaos Geroliminis, Claudia Bongiovanni, Mor Kaspi
Mireille El Gheche, Giovanni Chierchia