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

Keywords

Modified Bessel functions
Asymptotic expansion
Stokes phenomenon
Exponentially small expansions

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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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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

SP - 407

EP - 416

JO - Mathematica Æterna

JF - Mathematica Æterna

SN - 1314-3344

IS - 4

ER -

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

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