Representations for the extreme zeros of orthogonal polynomials

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

Representations for the extreme zeros of orthogonal polynomials

Erik A. van Doorn, N.D. van Foreest, Alexander I. Zeifman

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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.

Original language	Undefined
Place of Publication	Enschede
Publisher	University of Twente, Department of Applied Mathematics
Number of pages	9
Publication status	Published - Aug 2007

Publication series

Name	Memorandum / Department of Applied Mathematics
Publisher	University of Twente, Department of Computer Science
No.	LNCS4549/1850
ISSN (Print)	1874-4850
ISSN (Electronic)	1874-4850

Keywords

Birth-death process
IR-64326
MSC-60J80
MSC-42C05
EWI-10994
Interval of orthogonality
Decay parameter
METIS-241876
Three-terms recurrence relation

Access to Document

http://www.math.utwente.nl/publications

Cite this

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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.",

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series = "Memorandum / Department of Applied Mathematics",

publisher = "University of Twente, Department of Applied Mathematics",

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TY - BOOK

T1 - Representations for the extreme zeros of orthogonal polynomials

AU - van Doorn, Erik A.

AU - van Foreest, N.D.

AU - Zeifman, Alexander I.

PY - 2007/8

Y1 - 2007/8

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.

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.

KW - Birth-death process

KW - IR-64326

KW - MSC-60J80

KW - MSC-42C05

KW - EWI-10994

KW - Interval of orthogonality

KW - Decay parameter

KW - METIS-241876

KW - Three-terms recurrence relation

M3 - Report

T3 - Memorandum / Department of Applied Mathematics

BT - Representations for the extreme zeros of orthogonal polynomials

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -