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

TL;DR

This paper discusses Dirichlet's proof of the general convergence of Fourier series, correcting earlier errors by Cauchy, and provides a transcribed and annotated version of the original 1829 publication.

Contribution

It offers a detailed transcription of Dirichlet's original work on Fourier series convergence, including corrections and a comprehensive bibliography, clarifying historical mathematical developments.

Findings

Dirichlet proved the general convergence of Fourier series.

Corrections were made to Cauchy's earlier work on the topic.

The paper includes a complete transcription and bibliography of the original publication.

Abstract

Dirichlet proves the general convergence of Fourier series, after pointing out errors in an earlier attempt by Cauchy. We transcribed from Crelle's Journal (1829) with numerous typographical corrections, and added a completed bibliography. 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 avons transcrit de Crelle's journal (1829) avec de nombreuses corrections typographiques, et avons ajout\'e une bibliographie compl\`ete.