Geodesic
New Integral Equations for the Monic Hermite Polynomials
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 1, p. 7
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In this article, we are study the question of existence of integral equation for the monic $\mathcal{H}$ermite polynomials ${H}_{n}$, where the intervening real function does not depend on the index $n$, well-known by the linear functional $\mathscr{W}_{x}$ given by its moments ${H}_{n}(x)=\left〈\mathscr{W}_{x},t^{n}\right〉$, $n\geq 0$, $| x| \infty$. Also, we obtain some properties of the zeros of this intervening function. Furthermore, we obtain an integral representation of the Dirac mass $\delta _{x},$ for every real number $x$.
Classification : 33C45, 42C05
Keywords: linear functional, integral equation, integral representation on the real line, Hermite polynomials, Dawson function, Dirac mass 
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     author = {Karima Ali Khelil and Ridha Sfaxi and Ammar Boukhemis},
     title = {New {Integral} {Equations} for the {Monic} {Hermite} {Polynomials}},
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Karima Ali Khelil; Ridha Sfaxi; Ammar Boukhemis. New Integral Equations for the Monic Hermite Polynomials. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 1, p. 7 . http://geodesic.mathdoc.fr/item/KJM_2022_46_1_a0/