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Dirichlet proves the general convergence of Fourier series, after pointingout errors in an earlier attempt by Cauchy. We transcribed from Crelle'sJournal (1829) with numerous typographical corrections, and added a completedbibliography.  Dirichlet prouve la convergence g\'en\'erale de la s\'eries de Fourier,apr\`es avoir montr\'e des erreurs dans un essai par Cauchy. Nous avonstranscrit de Crelle's journal (1829) avec de nombreuses correctionstypographiques, et avons ajout\'e une bibliographie compl\`ete.

Sur la convergence des s\'eries trigonom\'etriques qui servent \`a repr\'esenter une fonction arbitraire entre des limites donn\'ees