New Integral Equations for the Monic Hermite Polynomials

Abstract

In this article, we are study the question of existence of integral equation for the monic Hermite polynomials Hn, where the intervening real function does not depend on the index n, well-known by the linear functional Wx given by its moments Hn(x) = ⟨Wx, tn⟩, n ≥ 0, ♣x♣ < ∞. Also, we obtain some properties of the zeros of this intervening function. Furthermore, we obtain an integral representation of the Dirac mass δx, for every real number x.