Asymptotic expansions of the generalized Bessel polynomials

R. Wong; J. M. Zhang

doi:10.1016/S0377-0427(97)00131-3

Asymptotic expansions of the generalized Bessel polynomials

R. Wong
, J. M. Zhang

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

10 Citations (Scopus)

Abstract

In this paper, we investigate the asymptotic behavior of the generalized Bessel polynomials y_n(z; a). Let z = α/(n + 1). We first derive infinite asymptotic expansions for y_n(z; a) when α lies in various regions of the complex plane, except when a is near ±i. Then we construct uniform asymptotic expansions for y_n(z; a) in neighborhoods of α = ±i. These expansions involve the Airy function and its derivative. Finally, we use these approximations to study the asymptotic behavior of the zeros of y_n(z; ) near α = i.

Original language	English
Pages (from-to)	87-112
Journal	Journal of Computational and Applied Mathematics
Volume	85
Issue number	1
DOIs	https://doi.org/10.1016/S0377-0427(97)00131-3
Publication status	Published - 6 Nov 1997

Research Keywords

Generalized Bessel polynomials
Steepest descent method
Uniform asymptotic expansions
Zeros

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title = "Asymptotic expansions of the generalized Bessel polynomials",

abstract = "In this paper, we investigate the asymptotic behavior of the generalized Bessel polynomials yn(z; a). Let z = α/(n + 1). We first derive infinite asymptotic expansions for yn(z; a) when α lies in various regions of the complex plane, except when a is near ±i. Then we construct uniform asymptotic expansions for yn(z; a) in neighborhoods of α = ±i. These expansions involve the Airy function and its derivative. Finally, we use these approximations to study the asymptotic behavior of the zeros of yn(z; ) near α = i.",

keywords = "Generalized Bessel polynomials, Steepest descent method, Uniform asymptotic expansions, Zeros",

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year = "1997",

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T1 - Asymptotic expansions of the generalized Bessel polynomials

AU - Wong, R.

AU - Zhang, J. M.

PY - 1997/11/6

Y1 - 1997/11/6

N2 - In this paper, we investigate the asymptotic behavior of the generalized Bessel polynomials yn(z; a). Let z = α/(n + 1). We first derive infinite asymptotic expansions for yn(z; a) when α lies in various regions of the complex plane, except when a is near ±i. Then we construct uniform asymptotic expansions for yn(z; a) in neighborhoods of α = ±i. These expansions involve the Airy function and its derivative. Finally, we use these approximations to study the asymptotic behavior of the zeros of yn(z; ) near α = i.

AB - In this paper, we investigate the asymptotic behavior of the generalized Bessel polynomials yn(z; a). Let z = α/(n + 1). We first derive infinite asymptotic expansions for yn(z; a) when α lies in various regions of the complex plane, except when a is near ±i. Then we construct uniform asymptotic expansions for yn(z; a) in neighborhoods of α = ±i. These expansions involve the Airy function and its derivative. Finally, we use these approximations to study the asymptotic behavior of the zeros of yn(z; ) near α = i.

KW - Generalized Bessel polynomials

KW - Steepest descent method

KW - Uniform asymptotic expansions

KW - Zeros

UR - https://www.scopus.com/pages/publications/0031556570

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0031556570&origin=recordpage

U2 - 10.1016/S0377-0427(97)00131-3

DO - 10.1016/S0377-0427(97)00131-3

M3 - RGC 21 - Publication in refereed journal

SN - 0377-0427

VL - 85

SP - 87

EP - 112

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1

ER -

Asymptotic expansions of the generalized Bessel polynomials

Abstract

Research Keywords

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