Sequences of twice-iterated ?w-Gould-Hopper Appell polynomials - Biricik, Neslihan; Cekim, Bayram; Ozarslan, Mehmet Ali (Taylor & Francis Ltd, 2024)
In this paper, we introduce general sequence of twice-iterated Delta(w) -(degenerate) Gould-Hopper Appell polynomials (TI-DGHAP) via discrete Delta(w)-Gould-Hopper Appell convolution. We obtain some of their characteristic properties such as explicit representation, determinantal representation, recurrence relation, lowering operator (LO), raising operator (RO), difference equation (DE), integro-partial lowering operator (IPLO), integro-partial raising operator (IPRO) and integro-partial difference equation (IPDE). As special cases of these general polynomials, we present TI degenerate Gould-Hopper Bernoulli polynomials, TI degenerate Gould-Hopper Poisson-Charlier polynomials, TI degenerate Gould-Hopper Boole polynomials and TI degenerate Gould-Hopper Poisson-Charlier-Boole polynomials. We also state their corresponding characteristic properties.
Keywords: Delta(w)-Gould-Hopper Appell polynomials; recurrence relation; shift operators; difference equations