On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters

Andrei Martínez-Finkelshtein; Pedro Martínez-González; Ramón Orive

doi:10.1016/S0377-0427(00)00654-3

On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters

Andrei Martínez-Finkelshtein, Pedro Martínez-González, Ramón Orive

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

31 Scopus citations

Abstract

We study the asymptotic zero distribution of Laguerre L_n^(αn) and generalized Bessel B_n^(αn) polynomials with the parameter α_n varying in such a way that the limit of α_n/n exists. Our approach is based on a non-hermitian orthogonality satisfied by these sequences of polynomials. In the cases that remain open we formulate the corresponding conjectures.

Original language	English
Pages (from-to)	477-487
Number of pages	11
Journal	Journal of Computational and Applied Mathematics
Volume	133
Issue number	1-2
DOIs	https://doi.org/10.1016/S0377-0427(00)00654-3
State	Published - 1 Aug 2001
Externally published	Yes

Keywords

Bessel polynomials
Equilibrium measure
Laguerre polynomials
Logarithmic potential
Non-hermitian orthogonality
Weak zero asymptotics

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/S0377-0427(00)00654-3

Cite this

@article{03fa175352ed44f89e7fb332d2ac7210,

title = "On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters",

abstract = "We study the asymptotic zero distribution of Laguerre Ln(αn) and generalized Bessel Bn(αn) polynomials with the parameter αn varying in such a way that the limit of αn/n exists. Our approach is based on a non-hermitian orthogonality satisfied by these sequences of polynomials. In the cases that remain open we formulate the corresponding conjectures.",

keywords = "Bessel polynomials, Equilibrium measure, Laguerre polynomials, Logarithmic potential, Non-hermitian orthogonality, Weak zero asymptotics",

author = "Andrei Mart{\'i}nez-Finkelshtein and Pedro Mart{\'i}nez-Gonz{\'a}lez and Ram{\'o}n Orive",

year = "2001",

month = aug,

day = "1",

doi = "10.1016/S0377-0427(00)00654-3",

language = "English",

volume = "133",

pages = "477--487",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "Elsevier B.V.",

number = "1-2",

}

TY - JOUR

T1 - On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters

AU - Martínez-Finkelshtein, Andrei

AU - Martínez-González, Pedro

AU - Orive, Ramón

PY - 2001/8/1

Y1 - 2001/8/1

N2 - We study the asymptotic zero distribution of Laguerre Ln(αn) and generalized Bessel Bn(αn) polynomials with the parameter αn varying in such a way that the limit of αn/n exists. Our approach is based on a non-hermitian orthogonality satisfied by these sequences of polynomials. In the cases that remain open we formulate the corresponding conjectures.

AB - We study the asymptotic zero distribution of Laguerre Ln(αn) and generalized Bessel Bn(αn) polynomials with the parameter αn varying in such a way that the limit of αn/n exists. Our approach is based on a non-hermitian orthogonality satisfied by these sequences of polynomials. In the cases that remain open we formulate the corresponding conjectures.

KW - Bessel polynomials

KW - Equilibrium measure

KW - Laguerre polynomials

KW - Logarithmic potential

KW - Non-hermitian orthogonality

KW - Weak zero asymptotics

UR - http://www.scopus.com/inward/record.url?scp=0035417493&partnerID=8YFLogxK

U2 - 10.1016/S0377-0427(00)00654-3

DO - 10.1016/S0377-0427(00)00654-3

M3 - Article

AN - SCOPUS:0035417493

SN - 0377-0427

VL - 133

SP - 477

EP - 487

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 1-2

ER -

On asymptotic zero distribution of Laguerre and generalized Bessel polynomials with varying parameters

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this