A note on the asymptotics of the modified Bessel functions on the Stokes lines

Abstract

We employ the exponentially improved asymptotic expansions of the confluent hypergeometric functions on the Stokes lines discussed by the author [Appl. Math. Sci. {\bf 7} (2013) 6601--6609] to give the analogous expansions of the modified Bessel functions $I_\nu(z)$ and $K_\nu(z)$ for large $z$ and finite $\nu$ on $\arg\,z=\pm\pi$ (and, in the case of $I_\nu(z)$, also on $\arg\,z=0$). Numerical results are presented to illustrate the accuracy of these expansions.