2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/95364We 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.Classical Analysis and ODEs42C10 (Primary) 30B50, 33C10 (Secondary)text