L'inauguration des s\'eries trigonom\'etriques dans la Th\'eorie analytique de la chaleur de Fourier et dans la controverse des cordes vibrantes

TL;DR

This paper analyzes the role of Fourier's book as an inaugural text in the development of trigonometric series within Fourier's heat theory and the vibrating strings controversy, using semiotic analysis to clarify the conditions for representing arbitrary functions.

Contribution

It demonstrates that Fourier's book is the sole inaugural text in this context and provides a semiotic analysis of how generality is expressed in the mathematical representations.

Findings

Fourier's book is identified as the only inaugural text.

Semiotic analysis clarifies conditions for representing functions with trigonometrical series.

The study enhances understanding of the conceptual foundations of Fourier's theory.

Abstract

Cet article applique les notions de texte et d'\'enonc\'e inaugural \`a la Th\'eorie analytique de la chaleur de Fourier et \`a la controverse des cordes vibrantes. Il \'etablit que seul le livre de Fourier est un texte inaugural. Il propose en outre une analyse s\'emiotique des modes d'expression de la g\'en\'eralit\'e qui permet dans chaque cas de clarifier les conditions d'introduction de la possibilit\'e de repr\'esenter une fonction arbitraire par des s\'eries trigonom\'etriques. (The inauguration of trigonometrical series in Fourier's Th\'eorie analytique de la chaleur and in the vibrating strings controversy) This paper applies the notions of inaugural text and statement to Fourier's Th\'eorie analytique de la chaleur and to the vibrating strings controversy. It establishes that only Fourier's book is an inaugural text. It presents also a semiotic analysis of the expression modes of generality which allows to clarify in both cases the conditions of introducing of the possibility to represent an arbitrary function by trigonometrical series.