Geodesic
An Operational Approach to the Generalized Rencontres Polynomials
Kragujevac Journal of Mathematics, Tome 46 (2022) no. 3, p. 461 .

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

In this paper, we study the umbral operators $ J $, $ M $ and $ N $ associated with the generalized rencontres polynomials $ D_n^{(m)}(x) $. We obtain their representations in terms of the differential operator $ \D_x $ and the shift operator $ E $. Then, by using these representations, we obtain some combinatorial and differential identities for the generalized rencontres polynomials. Finally, we extend these results to some related polynomials and, in particular, to the generalized permutation polynomials $ P_n^{(m)}(x) $ and the generalized arrangement polynomials $ A_n^{(m)}(x) $.
Classification : 05A19, 05A40, 05A15, 15A04
Keywords: umbral operator, Sheffer sequence, Appell sequence 
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     author = {Emanuele Munarini},
     title = {An {Operational} {Approach} to the {Generalized} {Rencontres} {Polynomials}},
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Emanuele Munarini. An Operational Approach to the Generalized Rencontres Polynomials. Kragujevac Journal of Mathematics, Tome 46 (2022) no. 3, p. 461 . http://geodesic.mathdoc.fr/item/KJM_2022_46_3_a9/