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

TL;DR

This paper derives and illustrates improved asymptotic expansions for the modified Bessel functions on Stokes lines, enhancing understanding of their behavior for large arguments.

Contribution

It provides the first exponentially improved asymptotic expansions of modified Bessel functions on Stokes lines, extending previous work on hypergeometric functions.

Findings

Numerical results confirm high accuracy of the new expansions.

Expansions are valid for large z and finite order nu on specified arguments.

Enhanced understanding of Bessel functions' asymptotics on 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.