Uniform asymptotics and zeros of the associated Pollaczek polynomials

Xiao-Min Huang; R. Wong

doi:10.1111/sapm.12292

Uniform asymptotics and zeros of the associated Pollaczek polynomials

Xiao-Min Huang^*
, R. Wong

^*Corresponding author for this work

Liu Bie Ju Centre for Mathematical Sciences

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

1 Citation (Scopus)

Abstract

Using a difference-equation method in a previous paper, we study the associated Pollaczek polynomials P^λ_n(x;a,b,c) defined by a three-term recurrence relation. Two asymptotic approximations are derived for these polynomials; one holds for x=1+t/n with -(a+b)<t and (a+b)>0, and the other holds for x=1+t/n with t in a neighborhood of t=-(a+b). An asymptotic formula is also provided for their largest zeros.

Original language	English
Pages (from-to)	625-646
Journal	Studies in Applied Mathematics
Volume	145
Issue number	4
Online published	11 Jan 2020
DOIs	https://doi.org/10.1111/sapm.12292
Publication status	Published - Nov 2020

Research Keywords

difference-equation method
turning point
uniform asymptotics
zeros

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title = "Uniform asymptotics and zeros of the associated Pollaczek polynomials",

abstract = "Using a difference-equation method in a previous paper, we study the associated Pollaczek polynomials Pλn(x;a,b,c) defined by a three-term recurrence relation. Two asymptotic approximations are derived for these polynomials; one holds for x=1+t/n with -(a+b)a+b)>0, and the other holds for x=1+t/n with t in a neighborhood of t=-(a+b). An asymptotic formula is also provided for their largest zeros.",

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author = "Xiao-Min Huang and R. Wong",

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T1 - Uniform asymptotics and zeros of the associated Pollaczek polynomials

AU - Huang, Xiao-Min

AU - Wong, R.

PY - 2020/11

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N2 - Using a difference-equation method in a previous paper, we study the associated Pollaczek polynomials Pλn(x;a,b,c) defined by a three-term recurrence relation. Two asymptotic approximations are derived for these polynomials; one holds for x=1+t/n with -(a+b)a+b)>0, and the other holds for x=1+t/n with t in a neighborhood of t=-(a+b). An asymptotic formula is also provided for their largest zeros.

AB - Using a difference-equation method in a previous paper, we study the associated Pollaczek polynomials Pλn(x;a,b,c) defined by a three-term recurrence relation. Two asymptotic approximations are derived for these polynomials; one holds for x=1+t/n with -(a+b)a+b)>0, and the other holds for x=1+t/n with t in a neighborhood of t=-(a+b). An asymptotic formula is also provided for their largest zeros.

KW - difference-equation method

KW - turning point

KW - uniform asymptotics

KW - zeros

UR - https://www.scopus.com/pages/publications/85077888873

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85077888873&origin=recordpage

U2 - 10.1111/sapm.12292

DO - 10.1111/sapm.12292

M3 - RGC 21 - Publication in refereed journal

SN - 0022-2526

VL - 145

SP - 625

EP - 646

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

IS - 4

ER -

Uniform asymptotics and zeros of the associated Pollaczek polynomials

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Research Keywords

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