Abstract
We employ the exponentially improved asymptotic expansions of the confluent hypergeometric functions on the Stokes lines discussed by the author [Appl. Math. Sci. 7 (2013) 6601–6609] to give the analogous expansions of the modified Bessel functions Iν(z) and Kν(z) for large z and finite ν on arg z = ±π (and, in the case of Iν(z), also on arg z = 0). Numerical results are presented to illustrate the accuracy of these expansions.
Original language | English |
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Pages (from-to) | 407-416 |
Number of pages | 10 |
Journal | Mathematica Æterna |
Volume | 7 |
Issue number | 4 |
Publication status | Published - 2017 |
Keywords
- Modified Bessel functions
- Asymptotic expansion
- Stokes phenomenon
- Exponentially small expansions