Note on the approximate values of Bessel's functions for large arguments

yo and Jt represent the Bessel functions of the first kind and of the zero and first order, respectively. G and Gx represent functions which are combinations of the Bessel functions of the first and second kinds, and have the property that the functions approach zero when the arguments become very large. The values of GQ(ix) and Gx{ix) in terms of the Bessel functions of the first and second kinds are given by the following equations: *