Some observations on a Kapteyn series

Details Some observations on a Kapteyn series Some observations on a Kapteyn series

2005-10-03

arxiv.org/abs/math/0510050v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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