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 Classifications: 33C45, 11B83, 12E10, 34A08
Keywords and phrases: Appell polynomials, Sheffer polynomials, Hermite-Kampé de Fériet polynomials, Gould Hopper polynomials, Monomiality principle.