Séminaire Lotharingien de Combinatoire, B76c (2017), 39 pp.
Lacunary Laguerre Series
from a Combinatorial Perspective
In recent work,
Babusci, Dattoli, G\'orska, and Penson
have presented a number of
lacunary generating functions
for the generalized Laguerre
i.e., series of the type
\sumn >= 0
cn L2n(\alpha)(x) tn,
by a method closely related to
This work is complemented here,
deriving many of their results by
interpreting Laguerre polynomials
combinatorially as enumerators for
(injective partial functions).
This combinatorial view pays in
that it suggests natural extensions
and gives a deeper insight into
the known formulas.
Received: December 21, 2016.
Accepted: February 25, 2017.
Final Version: March 22, 2017.
The following versions are available: