Convergent expansions of the Bessel functions in terms of elementary functions
Ver/
Fecha
2018Versión
Acceso abierto / Sarbide irekia
Tipo
Artículo / Artikulua
Versión
Versión aceptada / Onetsi den bertsioa
Impacto
|
10.1007/s10444-017-9543-y
Resumen
We consider the Bessel functions Jν (z) and Yν (z) for ν > −1/2 and
z ≥ 0. We derive a convergent expansion of Jν (z) in terms of the derivatives of
(sin z)/z, and a convergent expansion of Yν (z) in terms of derivatives of (1−cos z)/z,
derivatives of (1 − e−z)/z and (2ν, z). Both expansions hold uniformly in z in any
fixed horizontal strip and are accompanied by error bounds. The accuracy of ...
[++]
We consider the Bessel functions Jν (z) and Yν (z) for ν > −1/2 and
z ≥ 0. We derive a convergent expansion of Jν (z) in terms of the derivatives of
(sin z)/z, and a convergent expansion of Yν (z) in terms of derivatives of (1−cos z)/z,
derivatives of (1 − e−z)/z and (2ν, z). Both expansions hold uniformly in z in any
fixed horizontal strip and are accompanied by error bounds. The accuracy of the
approximations is illustrated with some numerical experiments. [--]
Materias
Bessel functions,
Convergent expansions,
Error bounds,
Uniform expansions
Editor
Springer US
Publicado en
Advances in Computational Mathematics (2018) 44:277–294
Notas
This is a post-peer-review, pre-copyedit version of an article published in Advances in Computational Mathematics. The final authenticated version is available online at: https://doi.org/10.1007/s10444-017-9543-y
Departamento
Universidad Pública de Navarra. Departamento de Ingeniería Matemática e Informática /
Nafarroako Unibertsitate Publikoa. Matematika eta Informatika Ingeniaritza Saila /
Universidad Pública de Navarra/Nafarroako Unibertsitate Publikoa. Institute for Advanced Materials and Mathematics - INAMAT2
Versión del editor
Entidades Financiadoras
This research was supported by the Spanish Ministry of "Economía y Competitividad",
project MTM2014-52859-P. The Universidad Pública de Navarra is acknowledged by its
financial support.