Generalisation de formules de type Waring

Abstract

We evaluate the symmetric functions $e_k$, $h_k$ and $p_k$ on the alphabet $\{x_r/(1-t{x}_r)\}$ by elementary methods and give the related generating functions. Our formulas lead to a new and short proof of an ex-conjecture of Lassalle, which was proved by Lascoux and Lassalle in the framework of $\lambda$-rings theory.