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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:
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
Descripción
Sumario: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.