Abstract
We consider the Bessel functions J ν (z) and Y ν (z) for R ν > −1/2 and R z ≥ 0. We derive a convergent expansion of J ν (z) in terms of the derivatives of \((\sin z)/z\), and a convergent expansion of Y ν (z) in terms of derivatives of \((1-\cos z)/z\), derivatives of (1 − e −z)/z and Γ(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.
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Acknowledgments
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. Professor Dmitrii Karp is acknowledged by his helpful comments.
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Communicated by: Yuesheng Xu
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López, J.L. Convergent expansions of the Bessel functions in terms of elementary functions. Adv Comput Math 44, 277–294 (2018). https://doi.org/10.1007/s10444-017-9543-y
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DOI: https://doi.org/10.1007/s10444-017-9543-y