Résumé: In this article, we are study the question of existence of integral equation for the monic Hermite polynomials H_n, where the intervening real function does not depend on the index n, well-known by the linear functional W_x given by its moments. Also, we obtain some properties of the zeros of this intervening function. Furthermore, we obtain an integral representation of the Dirac mass, for every real number x.

Résumé: In this paper, we are interested in the integral representation problem of the generalized Bessel linear functional B[a], well-known by the Pearson equation. By means of some integral estimation and technical results including important inequalities of the incomplete gamma function and the exponential integral, we obtain an integral representation of B[a]. The connection formula between B[a] and the classical Bessel linear functional B(a) allows us to obtain an integral representation of B(a).