Monotonicity of zeros of derivatives of Bessel functions
Recently Baricz et al., 2018 and Baricz and Singh 2018 gave two different proofs of the fact that the zeros of the nth derivative of the Bessel function of the first kind Jν(x) are all real when ν>n−1. We provide a third alternative proof. The authors of Baricz et al., 2018 conjectured that, for...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2025 |
| País: | Brasil |
| Institución: | Universidade Estadual Paulista (UNESP) |
| Repositorio: | Repositório Institucional da UNESP |
| Idioma: | inglés |
| OAI Identifier: | oai:repositorio.unesp.br:11449/302871 |
| Acceso en línea: | http://dx.doi.org/10.1016/j.jat.2024.106102 https://hdl.handle.net/11449/302871 |
| Access Level: | acceso abierto |
| Palabra clave: | Jensen polynomials Laguerre's theorem Laguerre–Pólya class Monotonicity of zeros Zeros of derivatives of the Bessel function |
| Sumario: | Recently Baricz et al., 2018 and Baricz and Singh 2018 gave two different proofs of the fact that the zeros of the nth derivative of the Bessel function of the first kind Jν(x) are all real when ν>n−1. We provide a third alternative proof. The authors of Baricz et al., 2018 conjectured that, for every n∈N, the positive zeros of Jν(n)(x) are increasing functions of the parameter ν, for ν∈(n−1,∞). We provide two apparently distinct proofs of the conjecture. |
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