Jñānābha‎, Vol. 49 (1) (2019), 80-88

GENERALIZED HERMITE POLYNOMIAL FAMILIES

Paolo Emilio Ricci

Section of Mathematics, International Telematic University UniNettuno
Corso Vittorio Emanuele II, 39, 00186 - Roma, Italia
Email:paoloemilioricci@gmail.com
(Received : May 29, 2019)


Abstract

In recent papers, new sets of Sheffer and Brenke polynomials based on higher order Bell numbers, and several integer sequences related to them have been studied.
In this article we .find families of Sheffer polynomials, including as a particular case generalized Hermite polynomial families, deriving their recurrence relations and differential equations, which are sometimes of fractional type.


2010 Mathematics Subject Classifications33C45, 11B83, 12E10, 34A08
Keywords and phrasesAppell polynomials, Sheffer polynomials, Hermite-Kampé de Fériet polynomials, Gould Hopper polynomials, Monomiality principle.