Some observations on a Kapteyn series

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We study the Kapteyn series $% %TCIMACRO{\dsum \limits_{n=1}^{\infty}}% %BeginExpansion {\displaystyle\sum\limits_{n=1}^{\infty}} %EndExpansion t^{n}\mathrm{J}_{n}(nz) $. We find a series representation in powers of $z$ and analyze its radius of convergence.

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Classical Analysis and ODEs, 42C10 (Primary) 30B50, 33C10 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/95364

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0510050
 http://arxiv.org/abs/math/0510050

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arXiv