A new generalization of Laguerre-based Appell polynomials with two parameters

BİRİCİK HEPSİSLER N., ÇEKİM B., Özarslan M. A.

Filomat, cilt.39, sa.26, ss.9347-9362, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 39 Sayı: 26
  • Basım Tarihi: 2025
  • Doi Numarası: 10.2298/fil2526347b
  • Dergi Adı: Filomat
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.9347-9362
  • Anahtar Kelimeler: determinant form, differential equations, Laguerre based-Appell polynomials
  • Gazi Üniversitesi Adresli: Evet

Özet

In this paper, we define a new generalization of Laguerre-based Appell polynomials with two parameters. We obtain a recurrence relation, a lowering operator, a integro-partial raising operator, a integro-partial differential equation for this new polynomial family. We introduce subpolynomials of these polynomials, namely Laguerre-based Hermite-Frobenius Euler polynomials, Laguerre-based Miller-Lee polynomials and generalizations of Laguerre-based Hermite polynomials and obtain various properties of them. We also show 3D graphs of these subfamilies and graphs of the distribution of their real roots.