Asymptotic formulae for the Lommel and Bessel functions and their derivatives

We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate represent...

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Detalles Bibliográficos
Autor principal: Aleksandrova, N. I.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2014
Materias:
Research Articles
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4448900/
https://www.ncbi.nlm.nih.gov/pubmed/26064539
http://dx.doi.org/10.1098/rsos.140176
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author Aleksandrova, N. I.
author_facet Aleksandrova, N. I.
author_sort Aleksandrova, N. I.
collection PubMed
description We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for what values of the parameters our representations have reasonable accuracy.
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spelling pubmed-44489002015-06-10 Asymptotic formulae for the Lommel and Bessel functions and their derivatives Aleksandrova, N. I. R Soc Open Sci Research Articles We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the same method, we obtain previously known approximate representations of the Nicholson type for Bessel functions and their first derivatives. We study also for what values of the parameters our representations have reasonable accuracy. The Royal Society Publishing 2014-10-08 /pmc/articles/PMC4448900/ /pubmed/26064539 http://dx.doi.org/10.1098/rsos.140176 Text en © 2014 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Research Articles
Aleksandrova, N. I.
Asymptotic formulae for the Lommel and Bessel functions and their derivatives
title Asymptotic formulae for the Lommel and Bessel functions and their derivatives
title_full Asymptotic formulae for the Lommel and Bessel functions and their derivatives
title_fullStr Asymptotic formulae for the Lommel and Bessel functions and their derivatives
title_full_unstemmed Asymptotic formulae for the Lommel and Bessel functions and their derivatives
title_short Asymptotic formulae for the Lommel and Bessel functions and their derivatives
title_sort asymptotic formulae for the lommel and bessel functions and their derivatives
topic Research Articles
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4448900/
https://www.ncbi.nlm.nih.gov/pubmed/26064539
http://dx.doi.org/10.1098/rsos.140176
work_keys_str_mv AT aleksandrovani asymptoticformulaeforthelommelandbesselfunctionsandtheirderivatives

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