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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.14295 |
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| _version_ | 1866915591468613632 |
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| author | Dunster, T. M. Gil, Amparo Ruiz-Antolin, Diego Segura, Javier |
| author_facet | Dunster, T. M. Gil, Amparo Ruiz-Antolin, Diego Segura, Javier |
| contents | Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-Δ_{1} n+\frac{3}{2} \leq a \leq Δ_{2} n$ for fixed arbitrary $Δ_{1} \in (0,1)$ and bounded positive $Δ_{2}$. For this parameter range at most one of the zeros is real, with the rest being complex conjugates. The new expansions are uniformly valid for all the zeros, and are shown to be highly accurate for moderate or large values of $n$. They are consequently used as initial values in a very efficient numerical algorithm designed to obtain the remaining complex zeros using Taylor series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14295 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform Asymptotic approximation and numerical evaluation of the Reverse Generalized Bessel Polynomial zeros Dunster, T. M. Gil, Amparo Ruiz-Antolin, Diego Segura, Javier Classical Analysis and ODEs 34E05, 33C10, 34M60, 34E20 Uniform asymptotic expansions are derived for the zeros of the reverse generalized Bessel polynomials of large degree $n$ and real parameter $a$. It is assumed that $-Δ_{1} n+\frac{3}{2} \leq a \leq Δ_{2} n$ for fixed arbitrary $Δ_{1} \in (0,1)$ and bounded positive $Δ_{2}$. For this parameter range at most one of the zeros is real, with the rest being complex conjugates. The new expansions are uniformly valid for all the zeros, and are shown to be highly accurate for moderate or large values of $n$. They are consequently used as initial values in a very efficient numerical algorithm designed to obtain the remaining complex zeros using Taylor series. |
| title | Uniform Asymptotic approximation and numerical evaluation of the Reverse Generalized Bessel Polynomial zeros |
| topic | Classical Analysis and ODEs 34E05, 33C10, 34M60, 34E20 |
| url | https://arxiv.org/abs/2510.14295 |