Representations for the extreme zeros of orthogonal polynomials

Erik A. van Doorn; Nicky D. van Foreest; Alexander I. Zeifman

doi:10.1016/j.cam.2009.02.051

Representations for the extreme zeros of orthogonal polynomials

Erik A. van Doorn^*, Nicky D. van Foreest, Alexander I. Zeifman

^*Corresponding author voor dit werk

Operations Management & Operations Research

Onderzoeksoutput: Article › Academic › peer review

8 Citaten (Scopus)

64 Downloads (Pure)

Samenvatting

We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth-death process (with killing) are displayed. (C) 2009 Elsevier B.V. All rights reserved.

Originele taal-2	English
Pagina's (van-tot)	847-851
Aantal pagina's	5
Tijdschrift	Journal of Computational and Applied Mathematics
Volume	233
Nummer van het tijdschrift	3
DOI's	https://doi.org/10.1016/j.cam.2009.02.051
Status	Published - 1-dec.-2009
Evenement	9th Conference on Orthogonal Polynomials, Special Functions and Applications - , France Duur: 2-jul.-2007 → 6-jul.-2007

Toegang tot document

10.1016/j.cam.2009.02.051

Representations for the extreme zeros of orthogonal polynomialsFinal publisher's version, 378 KBLicentie: Elsevier

Handle.net

Permanente koppeling

8 Citaties
1 Erratum

Corrigendum to "Representations for the extreme zeros of orthogonal polynomials" [J.Comput.Appl.Math.233(2009) 847–851]
van Doorn, E. A., van Foreest, N. D. & Zeifman, A. I., 15-mei-2013, In: Journal of Computational and Applied Mathematics. 244, blz. 155-156 2 blz.
Onderzoeksoutput

Open Access
Bestand
81 Downloads (Pure)

Citeer dit

@article{84b09db18fc64606881760f7b21030e0,

title = "Representations for the extreme zeros of orthogonal polynomials",

abstract = "We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth-death process (with killing) are displayed. (C) 2009 Elsevier B.V. All rights reserved.",

keywords = "Three-terms recurrence relation, Interval of orthogonality, Birth-death process, Decay parameter, BIRTH-DEATH PROCESSES, NONHOMOGENEOUS BIRTH, DECAY PARAMETER, BOUNDS",

author = "\{van Doorn\}, \{Erik A.\} and \{van Foreest\}, \{Nicky D.\} and Zeifman, \{Alexander I.\}",

year = "2009",

month = dec,

day = "1",

doi = "10.1016/j.cam.2009.02.051",

language = "English",

volume = "233",

pages = "847--851",

journal = "Journal of Computational and Applied Mathematics",

issn = "0377-0427",

publisher = "ELSEVIER SCIENCE BV",

number = "3",

note = "9th Conference on Orthogonal Polynomials, Special Functions and Applications ; Conference date: 02-07-2007 Through 06-07-2007",

}

TY - JOUR

T1 - Representations for the extreme zeros of orthogonal polynomials

AU - van Doorn, Erik A.

AU - van Foreest, Nicky D.

AU - Zeifman, Alexander I.

PY - 2009/12/1

Y1 - 2009/12/1

N2 - We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth-death process (with killing) are displayed. (C) 2009 Elsevier B.V. All rights reserved.

AB - We establish some representations for the smallest and largest zeros of orthogonal polynomials in terms of the parameters in the three-terms recurrence relation. As a corollary we obtain representations for the endpoints of the true interval of orthogonality. Implications of these results for the decay parameter of a birth-death process (with killing) are displayed. (C) 2009 Elsevier B.V. All rights reserved.

KW - Three-terms recurrence relation

KW - Interval of orthogonality

KW - Birth-death process

KW - Decay parameter

KW - BIRTH-DEATH PROCESSES

KW - NONHOMOGENEOUS BIRTH

KW - DECAY PARAMETER

KW - BOUNDS

U2 - 10.1016/j.cam.2009.02.051

DO - 10.1016/j.cam.2009.02.051

M3 - Article

SN - 0377-0427

VL - 233

SP - 847

EP - 851

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 3

T2 - 9th Conference on Orthogonal Polynomials, Special Functions and Applications

Y2 - 2 July 2007 through 6 July 2007

ER -

Representations for the extreme zeros of orthogonal polynomials

Samenvatting

Toegang tot document

Handle.net

Vingerafdruk

Onderzoekersoutput

Corrigendum to "Representations for the extreme zeros of orthogonal polynomials" [J.Comput.Appl.Math.233(2009) 847–851]

Citeer dit