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. Dans-la-première-partie, nous considérons le calcul de certaines intégrales de type Selberg et leurs limites lorsque le nombre de variables tend vers l'infini. Dans le cas général, on montre que le résultat s'exprime comme un produit dont le nombre de facteurs ne dépend pas du nombre de variables (sous certaines conditions) Si la puissance du déterminant de Vandermonde vaut 2, il est possible de calculer la limite de ces intégrales lorsque le nombre de variables tend vers l'infini à l'aide d'opérateurs liés à l

. Dans-la-seconde-partie, nous étudions les propriétés de dépendance linéaire de familles de fonctions obtenues par intégrales itérées et donnons un critère qui permet d'assurer l'indépendance linéaire d'une famille infinie de fonctions à partir de l'étude des relations entre les fonctions obtenues par intégrales simples, Nous montrons comment construire effectivement les corps de germes de fonctions analytiques nécessaires et en donnons quelques exemples qui permettent d'étendre les résultats connus sur les hyperlogarithmes

. Ensuite, algèbre libre dans le but d'appliquer la factorisation de Schützenberger. Nous rappelons quelques résultats classiques, puis nous intéressons à la famille obtenue à partir des mots de Lyndon. Celle-ci ne permet pas d'écrire la factorisation qui nous intéresse mais nous précisons les caractéristiques de sa famille duale, Enfin, nous donnons un critère relatif à deux familles en dualité assurant que l'on peut écrire cette factorisation

. Mots-clefs, Combinatoire algébrique, Intégrales itérées, Intégrale de Selberg, Produits de mélange , Théorème de Cartier-Milnor-Moore