Séminaire Lotharingien de Combinatoire, B76b (2017), 19 pp.
Danilo Babusci, Giuseppe Dattoli, Katarzyna Górska and Karol Penson
Lacunary Generating Functions for the Laguerre Polynomials
Symbolic methods of umbral nature play an important and increasing
role in the theory of special functions and in related fields like
combinatorics. We discuss an application of these methods to the
theory of lacunary generating functions for the Laguerre polynomials
for which we give a number of new closed form expressions. We present
furthermore the different possibilities offered by the method we have
developed, with particular emphasis on their link to a new family of
special functions and with previous formulations, associated with the
theory of quasi monomials.
Received: May 7, 2013.
Revised: July 28, 2016.
Accepted: February 12, 2017.
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