A uniform asymptotic expansion for the jacobi polynomials with explicit remainder

R. Wong; J. -M. Zhang

doi:10.1080/00036819608840441

A uniform asymptotic expansion for the jacobi polynomials with explicit remainder

R. Wong
, J. -M. Zhang

Department of Mathematics

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

4 Citations (Scopus)

Abstract

A new asymptotic expansion is derived for the Jacobi polynonmial P_n^(α,β)(cos θ) asn → ∞ which holds uniformly for Θ ∈ [0, π/2]. An explicit expression is also given for the error term associated with the expansion. Our approach begins with a contour integral representation, followed by a suitable canonical transformation

Original language	English
Pages (from-to)	17-29
Journal	Applicable Analysis
Volume	61
Issue number	1-2
DOIs	https://doi.org/10.1080/00036819608840441
Publication status	Published - 1996

Research Keywords

Asymptotic series
Beahel funclions
Charlier polynominls
Legendre series

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10.1080/00036819608840441

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title = "A uniform asymptotic expansion for the jacobi polynomials with explicit remainder",

abstract = "A new asymptotic expansion is derived for the Jacobi polynonmial Pn(α,β)(cos θ) asn → ∞ which holds uniformly for Θ ∈ [0, π/2]. An explicit expression is also given for the error term associated with the expansion. Our approach begins with a contour integral representation, followed by a suitable canonical transformation",

keywords = "Asymptotic series, Beahel funclions, Charlier polynominls, Legendre series",

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year = "1996",

doi = "10.1080/00036819608840441",

language = "English",

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journal = "Applicable Analysis",

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publisher = "Taylor \& Francis",

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TY - JOUR

T1 - A uniform asymptotic expansion for the jacobi polynomials with explicit remainder

AU - Wong, R.

AU - Zhang, J. -M.

PY - 1996

Y1 - 1996

N2 - A new asymptotic expansion is derived for the Jacobi polynonmial Pn(α,β)(cos θ) asn → ∞ which holds uniformly for Θ ∈ [0, π/2]. An explicit expression is also given for the error term associated with the expansion. Our approach begins with a contour integral representation, followed by a suitable canonical transformation

AB - A new asymptotic expansion is derived for the Jacobi polynonmial Pn(α,β)(cos θ) asn → ∞ which holds uniformly for Θ ∈ [0, π/2]. An explicit expression is also given for the error term associated with the expansion. Our approach begins with a contour integral representation, followed by a suitable canonical transformation

KW - Asymptotic series

KW - Beahel funclions

KW - Charlier polynominls

KW - Legendre series

UR - https://www.scopus.com/pages/publications/0012689373

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0012689373&origin=recordpage

U2 - 10.1080/00036819608840441

DO - 10.1080/00036819608840441

M3 - RGC 21 - Publication in refereed journal

SN - 0003-6811

VL - 61

SP - 17

EP - 29

JO - Applicable Analysis

JF - Applicable Analysis

IS - 1-2

ER -

A uniform asymptotic expansion for the jacobi polynomials with explicit remainder

Abstract

Research Keywords

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