Geodesic
Complex Hermite polynomials: their generating functions via Lie algebra representation and operational methods
Novi Sad Journal of Mathematics, Tome 54 (2024) no. 1.

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The purpose of this paper is to get new generating relations of the complex Hermite polynomials $H_{p,q}\left ( z,z^{*} \right )$ by extending the realization $\uparrow_{\omega,\mu}$ to study multiplier representations of a Lie group G(0,1). Also, we establish new operational formulas involving the polynomials $H_{p,q}\left ( z,z^{*} \right )$ and we will use them in a simple way to obtain new generating functions for the polynomials $H_{p,q}\left ( z,z^{*} \right )$. Also, we derive some special cases which are worth interest.
Publié le :
DOI : 10.30755/NSJOM.13700
Classification : 33C45, 33C50, 33C80
Keywords: complex Hermite polynomials, Lie algebra, operational methods, generating relations 
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     title = {Complex {Hermite} polynomials: their generating functions via {Lie} algebra representation and operational methods},
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Mohannad J. S. Shahwan; Maged G. Sud; Jihad A. Younis. Complex Hermite polynomials: their generating functions via Lie algebra representation and operational methods. Novi Sad Journal of Mathematics, Tome 54 (2024) no. 1. doi : 10.30755/NSJOM.13700. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.13700/

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