Geodesic
Lacunary Laguerre Series from a Combinatorial Perspective
Séminaire lotharingien de combinatoire, Tome 76 (2016-2018)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

In recent work, Babusci, Dattoli, G\'orska, and Penson have presented a number of lacunary generating functions for the generalized Laguerre polynomials Ln(\alpha)(x), i.e., series of the type \sumn >= 0 cn L2n(\alpha)(x) tn, by a method closely related to umbral calculus. This work is complemented here, deriving many of their results by interpreting Laguerre polynomials combinatorially as enumerators for discrete structures (injective partial functions). This combinatorial view pays in that it suggests natural extensions and gives a deeper insight into the known formulas. 

@article{SLC_2016-2018_76_a2,
     author = {Volker Strehl},
     title = {Lacunary {Laguerre} {Series} from a {Combinatorial} {Perspective}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {76},
     year = {2016-2018},
     url = {http://geodesic.mathdoc.fr/item/SLC_2016-2018_76_a2/}
}
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Volker Strehl. Lacunary Laguerre Series from a Combinatorial Perspective. Séminaire lotharingien de combinatoire, Tome 76 (2016-2018). http://geodesic.mathdoc.fr/item/SLC_2016-2018_76_a2/