Asymptotic Approximations of Jacobi Functions and Their Zeros with Error Bounds期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Asymptotic Approximations of Jacobi Functions and Their Zeros with Error Bounds

Authors:	Xiao Feng Zhu Xiu Chun Li

Institution:	(1) Department of Basic Science, Beijing Institute of Graphic Communication, Beijing 102600, P. R. China

Abstract:	The study of zeros of orthogonal functions is an important topic. In this paper, by improving the middle variable x(t), we've got a new form of asymptotic approximation, completed with error bounds, it is constructed for the Jacobi functions $\varphi ^{{{\left( {\alpha ,\beta } \right)}}}_{\mu } {\left( t \right)}{\left( {\alpha > - 1} \right)}{\text{as}}\mu \to + \infty$ . Besides, an accurate approximation with error bounds is also constructed correspondingly for the zeros t _μ,s of $\varphi ^{{{\left( {\alpha ,\beta } \right)}}}_{\mu } {\left( t \right)}{\left( {\alpha \geqslant 0} \right)}{\text{as}}\mu \to + \infty$ , uniformly with respect to s = 1, 2, . . . . Supported by Developing Key Subject Item of Beijing

Keywords:	Asymptotic approximation Jacobi function Zero Error bounds
本文献已被维普 SpringerLink 等数据库收录！