Sequences of twice-iterated Δw-Gould–Hopper Appell polynomials

Abstract

In this paper, we introduce general sequence of twice-iterated [Formula: see text]-(degenerate) Gould–Hopper Appell polynomials (TI-DGHAP) via discrete [Formula: see text]-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

• -Gould–Hopper Appell polynomials
• recurrence relation
• shift operators
• difference equations
• Primary 33C65
• Secondary 11B83