Error bounds for the asymptotic expansions of the Jacobi polynomials
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866912523437998080 |
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| author | Huang, Xiao-Min Lin, Yu Wang, Xiang-Sheng Wong, R. |
| author_facet | Huang, Xiao-Min Lin, Yu Wang, Xiang-Sheng Wong, R. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_04520 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Error bounds for the asymptotic expansions of the Jacobi polynomials Huang, Xiao-Min Lin, Yu Wang, Xiang-Sheng Wong, R. Classical Analysis and ODEs 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. |
| title | Error bounds for the asymptotic expansions of the Jacobi polynomials |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2508.04520 |