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

Biricik N., ÇEKİM B., Özarslan M. A.

Journal of Taibah University for Science, cilt.18, sa.1, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1080/16583655.2023.2286714
  • Dergi Adı: Journal of Taibah University for Science
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Directory of Open Access Journals
  • Anahtar Kelimeler: $ \Delta _{w} $ Δw-Gould–Hopper Appell polynomials, difference equations, recurrence relation, shift operators
  • Gazi Üniversitesi Adresli: Evet

Özet

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.