Some asymptotic formulae for cylindrical Bessel functions

Asymptotic formulae, convenient for numerical work, are derived for cylindrical Bessel functions of the first, second and third kinds, for modified Bessel functions of the first and second kinds of complex argument and real order, and for their derivatives. These formulae are valid when both argument and order go to infinity simultaneously, subject to a certain law of growth. The formulae may be used to compute the zeros of all the Bessel functions and their derivatives.