Asymptotic expansions for the radii of starlikeness of normalised Bessel functions

Árpád Baricz; Gergő Nemes

doi:10.1016/j.jmaa.2020.124624

Asymptotic expansions for the radii of starlikeness of normalised Bessel functions

Árpád Baricz
, Gergő Nemes^*

^*Corresponding author for this work

Babes-Bolyai University
Óbuda University
Alfréd Rényi Institute of Mathematics

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

3 Scopus citations

Abstract

The asymptotic behaviour, with respect to the large order, of the radii of starlikeness of two types of normalised Bessel functions is considered. We derive complete asymptotic expansions for the radii of starlikeness and provide recurrence relations for the coefficients of these expansions. The proofs rely on the notion of Rayleigh sums and asymptotic inversion. The techniques employed in the paper could be useful to treat similar problems where inversion of asymptotic expansions is involved.

Original language	English
Article number	124624
Journal	Journal of Mathematical Analysis and Applications
Volume	494
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2020.124624
State	Published - 15 Feb 2021
Externally published	Yes

Keywords

Asymptotic expansions
Bessel functions
Radius of starlikeness
Rayleigh sums
Zeros of Bessel functions

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10.1016/j.jmaa.2020.124624

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title = "Asymptotic expansions for the radii of starlikeness of normalised Bessel functions",

abstract = "The asymptotic behaviour, with respect to the large order, of the radii of starlikeness of two types of normalised Bessel functions is considered. We derive complete asymptotic expansions for the radii of starlikeness and provide recurrence relations for the coefficients of these expansions. The proofs rely on the notion of Rayleigh sums and asymptotic inversion. The techniques employed in the paper could be useful to treat similar problems where inversion of asymptotic expansions is involved.",

keywords = "Asymptotic expansions, Bessel functions, Radius of starlikeness, Rayleigh sums, Zeros of Bessel functions",

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AU - Nemes, Gergő

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N2 - The asymptotic behaviour, with respect to the large order, of the radii of starlikeness of two types of normalised Bessel functions is considered. We derive complete asymptotic expansions for the radii of starlikeness and provide recurrence relations for the coefficients of these expansions. The proofs rely on the notion of Rayleigh sums and asymptotic inversion. The techniques employed in the paper could be useful to treat similar problems where inversion of asymptotic expansions is involved.

AB - The asymptotic behaviour, with respect to the large order, of the radii of starlikeness of two types of normalised Bessel functions is considered. We derive complete asymptotic expansions for the radii of starlikeness and provide recurrence relations for the coefficients of these expansions. The proofs rely on the notion of Rayleigh sums and asymptotic inversion. The techniques employed in the paper could be useful to treat similar problems where inversion of asymptotic expansions is involved.

KW - Asymptotic expansions

KW - Bessel functions

KW - Radius of starlikeness

KW - Rayleigh sums

KW - Zeros of Bessel functions

UR - https://www.scopus.com/pages/publications/85091966381

U2 - 10.1016/j.jmaa.2020.124624

DO - 10.1016/j.jmaa.2020.124624

M3 - 文章

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SN - 0022-247X

VL - 494

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

M1 - 124624

ER -

Asymptotic expansions for the radii of starlikeness of normalised Bessel functions

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Keywords

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