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


Biricik N., ÇEKİM B., Özarslan M. A.

Journal of Taibah University for Science, vol.18, no.1, 2024 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.1080/16583655.2023.2286714
  • Journal Name: Journal of Taibah University for Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Keywords: $ \Delta _{w} $ Δw-Gould–Hopper Appell polynomials, difference equations, recurrence relation, shift operators
  • Gazi University Affiliated: Yes

Abstract

In this paper, we introduce general sequence of twice-iterated (Formula presented.) -(degenerate) Gould–Hopper Appell polynomials (TI-DGHAP) via discrete (Formula presented.) -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.