Séminaire Lotharingien de Combinatoire, B76b (2017), 19 pp.

Danilo Babusci, Giuseppe Dattoli, Katarzyna Górska and Karol Penson

Lacunary Generating Functions for the Laguerre Polynomials

Abstract. 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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