Darboux-type formula for Jacobi biorthogonal polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914567244742656 |
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| author | Lin, Zhaofeng Wang, Kai Zheng, Zhanhang |
| author_facet | Lin, Zhaofeng Wang, Kai Zheng, Zhanhang |
| contents | In this paper, we study the asymptotic behavior of Jacobi biorthogonal polynomials. A Darboux-type formula is established using the method of steepest descent. In the proof, we construct an appropriate contour to apply the Rodrigues formula. Our result reduces to the classical Darboux formula in the orthogonal case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14669 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Darboux-type formula for Jacobi biorthogonal polynomials Lin, Zhaofeng Wang, Kai Zheng, Zhanhang Classical Analysis and ODEs 33C45 (Primary) 41A60, 42C05, 30E20 (Secondary) In this paper, we study the asymptotic behavior of Jacobi biorthogonal polynomials. A Darboux-type formula is established using the method of steepest descent. In the proof, we construct an appropriate contour to apply the Rodrigues formula. Our result reduces to the classical Darboux formula in the orthogonal case. |
| title | Darboux-type formula for Jacobi biorthogonal polynomials |
| topic | Classical Analysis and ODEs 33C45 (Primary) 41A60, 42C05, 30E20 (Secondary) |
| url | https://arxiv.org/abs/2605.14669 |