Geodesic
New Integral Equations for the Monic Hermite Polynomials
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 1, p. 7

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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     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/