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

Research output: Contribution to journal › Article › peer-review

297 Downloads (Pure)

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

Access to Document

Paris_ANoteOnTheAsymptoticsOfTheModifiedBesselFunctions_Published_2017Final published version, 127 KBLicence: CC BY

https://www.longdom.org/articles/a-note-on-the-asymptotics-of-the-modified-bessel-functions-on-the-stokes-lines.pdfLicence: CC BY

Cite this

@article{0dfefcff75fd4b7e966ef26245e4a28e,

title = "A note on the asymptotics of the modified Bessel functions on the Stokes lines",

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.",

author = "Paris, \{R. B.\}",

year = "2017",

language = "English",

volume = "7",

pages = "407--416",

journal = "Mathematica {\AE}terna",

issn = "1314-3344",

number = "4",

}

TY - JOUR

T1 - A note on the asymptotics of the modified Bessel functions on the Stokes lines

AU - Paris, R. B.

PY - 2017

Y1 - 2017

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

SN - 1314-3344

VL - 7

SP - 407

EP - 416

JO - Mathematica Æterna

JF - Mathematica Æterna

IS - 4

ER -

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

Abstract

Keywords

Access to Document

Fingerprint

Cite this