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...

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Detalles Bibliográficos
Autores: Dimitrov, Dimitar K. [UNESP], Lun, Yen Chi [UNESP]
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
Descripción
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.