Geodesic
A New Class of Laguerre-Based Generalized Hermite-Euler Polynomials and its Properties
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 1, p. 89 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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The special polynomials of more than one variable provide new means of analysis for the solutions of a wide class of partial differential equations often encountered in physical problems. Motivated by their importance and potential for applications in a variety of research fields, recently, numerous polynomials and their extensions have been introduced and investigated. In this paper, we introduce a new family of Laguerre-based generalized Hermite-Euler polynomials, which are related to the Hermite, Laguerre and Euler polynomials and numbers. The results presented in this paper are based upon the theory of the generating functions. We derive summation formulas and related bilateral series associated with the newly introduced generating function. We also point out that the results presented here, being very general, can be specialized to give many known and new identities and formulas involving relatively simple numbers and polynomials.
Classification : 11B68, 33C45, 33C90 33C05
Keywords: hermite polynomials, Laguerre polynomials, generalized Euler polynomials, Laguerre-based generalized Hermite-Euler polynomials, summation formulae, bilateral series 
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     author = {N. U. Khan and T. Usman and W. A. Khan},
     title = {A {New} {Class} of {Laguerre-Based} {Generalized} {Hermite-Euler} {Polynomials} and its {Properties}},
     journal = {Kragujevac Journal of Mathematics},
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N. U. Khan; T. Usman; W. A. Khan. A New Class of Laguerre-Based Generalized Hermite-Euler Polynomials and its Properties. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 1, p. 89 . http://geodesic.mathdoc.fr/item/KJM_2020_44_1_a5/