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

R. B. Paris

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. 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 = ±π (and, in the case of I_ν(z), also on arg z = 0). Numerical results are presented to illustrate the accuracy of these expansions.

Original language	English
Pages (from-to)	407-416
Number of pages	10
Journal	Mathematica Æterna
Volume	7
Issue number	4
Publication status	Published - 2017

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Paris, R. B. (2017). A note on the asymptotics of the modified Bessel functions on the Stokes lines. Mathematica Æterna, 7(4), 407-416. https://www.longdom.org/articles/a-note-on-the-asymptotics-of-the-modified-bessel-functions-on-the-stokes-lines.pdf

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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. 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.",

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AB - 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.

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