复域上Jacobi多项式的一致渐近展开式

Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences Pub Date : 2004-09-08 DOI:10.1098/rspa.2004.1296

R. Wong, Yuqiu Zhao

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引用次数: 8

摘要

在正交性区间[- 1,1]内的雅可比多项式Pnα，β)(z)的行为与区间外的行为之间建立了一个渐近公式。这个公式所涉及的两个无穷级数被证明是指数改进的渐近展开式。本文所采用的方法也适用于其他正交多项式的情况，如Hermite和Laguerre。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Uniform asymptotic expansion of the Jacobi polynomials in a complex domain

An asymptotic formula is found that links the behaviour of the Jacobi polynomial Pnα,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.

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Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences

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