Error bounds for the asymptotic expansions of the Jacobi polynomials
Classical Analysis and ODEs
2025-08-07 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2508.04520,
title = {Error bounds for the asymptotic expansions of the Jacobi polynomials},
author = {Xiao-Min Huang and Yu Lin and Xiang-Sheng Wang and R. Wong},
journal= {arXiv preprint arXiv:2508.04520},
year = {2025}
}