标题： 雅可比多项式的渐近展开的误差界 显示英文标题

标题： Error bounds for the asymptotic expansions of the Jacobi polynomials

摘要： 本文旨在利用积分方法，推导雅可比多项式当次数趋于无穷时渐近展开的显式且可计算的误差界。 分析集中在这些多项式的外部或振荡区域。 引入了一种新技巧，以解决雅可比多项式积分表示中相位函数的对数奇异性所带来的挑战。 还开发了一个递推公式，用于计算渐近展开中的系数。 显示英文摘要

摘要： This paper aims to derive explicit and computable error bounds for the asymptotic expansion of the Jacobi polynomials as their degree approaches infinity, using an integral method. The analysis focuses on the outer or oscillatory region of these polynomials. A novel technique is introduced to address the challenges posed by the logarithmic singularity in the phase function of the integral representation of Jacobi polynomials. A recurrence formula is also developed to compute the coefficients in the asymptotic expansions.