A derivative-based extension of Gegenbauer polynomials in two variables

Ada Ö., DUMAN E.

Nuclear Physics B, vol.1025, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 1025
  • Publication Date: 2026
  • Doi Number: 10.1016/j.nuclphysb.2026.117393
  • Journal Name: Nuclear Physics B
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Chemical Abstracts Core, INSPEC, MathSciNet, zbMATH, Directory of Open Access Journals
  • Keywords: 2020 mathematics subject classification, 33C45 Gegenbauer polynomials, 33E20, Generating function, Recurrence relation, Symmetry identity
  • Gazi University Affiliated: Yes

Abstract

In this paper, a new class of two-variable Gegenbauer-type polynomials is introduced via a derivative-based construction. The definition incorporates an additional variable through finite sums involving higher-order derivatives of classical Gegenbauer polynomials with shifted parameters. Explicit representation and a generating function are obtained, leading to recurrence relations, differential relations, and an integral representation. Several addition formulas and properties involving Stirling numbers and power sums are also derived. Furthermore, new relations are established, leading to families of bilinear and bilateral generating functions. These results provide a systematic analytic description of the two-variable Gegenbauer polynomials.