Uniform asymptotic expansion of the Jacobi polynomials in a complex domain

R. Wong; Yu-Qiu Zhao

doi:10.1098/rspa.2004.1296

Uniform asymptotic expansion of the Jacobi polynomials in a complex domain

R. Wong, Yu-Qiu Zhao

Department of Mathematics

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

9 Citations (Scopus)

Abstract

An asymptotic formula is found that links the behaviour of the Jacobi polynomial Pn(α,β)(z) in the interval of orthogonality [-1,1] with that outside the interval. The two infinite series involved in this formula are shown to be exponentially improved asymptotic expansions. The method used in this paper can also be adopted in other cases of orthogonal polynomials such as Hermite and Laguerre. © 2004 The Royal Society.

Original language	English
Pages (from-to)	2569-2586
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	460
Issue number	2049
DOIs	https://doi.org/10.1098/rspa.2004.1296
Publication status	Published - 8 Sept 2004

Research Keywords

Complex domain
Exponential improvement
Jacobi polynomials
Uniform asymptotic expansion

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AU - Zhao, Yu-Qiu

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N2 - An asymptotic formula is found that links the behaviour of the Jacobi polynomial Pn(α,β)(z) in the interval of orthogonality [-1,1] with that outside the interval. The two infinite series involved in this formula are shown to be exponentially improved asymptotic expansions. The method used in this paper can also be adopted in other cases of orthogonal polynomials such as Hermite and Laguerre. © 2004 The Royal Society.

AB - An asymptotic formula is found that links the behaviour of the Jacobi polynomial Pn(α,β)(z) in the interval of orthogonality [-1,1] with that outside the interval. The two infinite series involved in this formula are shown to be exponentially improved asymptotic expansions. The method used in this paper can also be adopted in other cases of orthogonal polynomials such as Hermite and Laguerre. © 2004 The Royal Society.

KW - Complex domain

KW - Exponential improvement

KW - Jacobi polynomials

KW - Uniform asymptotic expansion

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DO - 10.1098/rspa.2004.1296

M3 - RGC 21 - Publication in refereed journal

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SP - 2569

EP - 2586

JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

IS - 2049

ER -

Uniform asymptotic expansion of the Jacobi polynomials in a complex domain

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Research Keywords

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