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 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 languageEnglish
Pages (from-to)407-416
Number of pages10
JournalMathematica Æterna
Volume7
Issue number4
Publication statusPublished - 2017

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Modified Bessel Functions
Stokes
Confluent Hypergeometric Function
Line
Asymptotic Expansion
Numerical Results

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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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A note on the asymptotics of the modified Bessel functions on the Stokes lines. / Paris, R. B.

In: Mathematica Æterna, Vol. 7, No. 4, 2017, p. 407-416.

Research output: Contribution to journalArticle

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AU - Paris, R. B.

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N2 - 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.

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.

M3 - Article

VL - 7

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EP - 416

JO - Mathematica Æterna

JF - Mathematica Æterna

SN - 1314-3344

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