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arXiv · 1708.09656

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

R B Paris
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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 $I_ν(z)$ and $K_ν(z)$ for large $z$ and finite $ν$ on $\arg\,z=\pmπ$ (and, in the case of $I_ν(z)$, also on $\arg\,z=0$). Numerical results are presented to illustrate the accuracy of these expansions.

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R B Paris. 2017-09-02. A note on the asymptotics of the modified Bessel functions on the Stokes lines. https://arxiv.org/abs/1708.09656

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