A new perspective on generalized Laguerre polynomials

DUMAN E.

Demonstratio Mathematica, cilt.58, sa.1, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 58 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1515/dema-2025-0162
  • Dergi Adı: Demonstratio Mathematica
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: generalized Laguerre polynomials, generating function, recurrence relation, summation formula
  • Gazi Üniversitesi Adresli: Evet

Özet

This article introduces two-variable polynomials constructed with generalized Laguerre polynomials. The study focuses on deriving generating function relationships, establishing closed-form summation formulas, and proving a symmetry identity for the proposed polynomials. In addition, a theorem concerning bilinear and bilateral generating functions is rigorously established. The connections between the newly defined polynomials and other well-known polynomial families are also explored, highlighting their potential to unify and extend existing mathematical frameworks. These findings provide a comprehensive perspective on the theoretical significance and applicability of the proposed polynomials in advanced mathematical research.