Truncated-Exponential-Based General-Appell Polynomials

Özat Z., ÇEKİM B., Özarslan M. A., Costabile F. A.

Mathematics, cilt.13, sa.8, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 13 Sayı: 8
  • Basım Tarihi: 2025
  • Doi Numarası: 10.3390/math13081266
  • Dergi Adı: Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Anahtar Kelimeler: Appell polynomials, bivariate Appell polynomials, truncated exponential polynomials
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, a new and general form of truncated-exponential-based general-Appell polynomials is introduced using the two-variable general-Appell polynomials. For this new polynomial family, we present an explicit representation, recurrence relation, shift operators, differential equation, determinant representation, and some other properties. Finally, two special cases of this family, truncated-exponential-based Hermite-type and truncated-exponential-based Laguerre–Frobenius Euler polynomials, are introduced and their corresponding properties are obtained.