Publication: Convergent expansions of the Bessel functions in terms of elementary functions
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Date
2018
Director
Publisher
Springer US
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión aceptada / Onetsi den bertsioa
Project identifier
MINECO//MTM2014-52859-P/ES/
Abstract
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.
Keywords
Bessel functions, Convergent expansions, Error bounds, Uniform expansions
Department
Matematika eta Informatika Ingeniaritza / Institute for Advanced Materials and Mathematics - INAMAT2 / Ingeniería Matemática e Informática
Faculty/School
Degree
Doctorate program
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Funding entities
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.
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