Note on the Asymptotic Expansion of the Mod- ified Bessel Function of the Second Kind

ura is usually the least term (in absolute value) of the series. Since the converging factor Rp/up may itself be developed as an asymptotic series, it is convenient to discuss this quantity rather than the remainder term. In a treatment due to Dingle a general theory of asymptotic expansions and their converging factors [2] is applied to the hypergeometric function [3], special cases of which are the modified Bessel functions of the first and second kinds. The formula relevant to the latter case is as follows