Structural Properties and Determinant Representations of Fubini-Fibonacci-Appell Polynomials in the Framework of Golden Calculus
Waseem Ahmad Khan, Can Kizilates, Khidir Shaib Mohamed, Naglaa Mohammed
article (Uluslararası, Hakemli) | Yazar(lar): Waseem Ahmad Khan, Can Kizilates, Khidir Shaib Mohamed, Naglaa Mohammed | Yıl: 2026 | Dergi/Kurum: SYMMETRY-BASEL | İndeks: WOS.SCI | DOI: 10.3390/sym18061064 | Anahtar Kelimeler: Golden calculus, Fubini polynomials, Fubini-Fibonacci polynomials, generating functions, Appel
In this paper, we introduce a novel class of Fubini-Fibonacci-Appell polynomials within the framework of Golden calculus. Utilizing generating function techniques and fibonomial convolution methods, we establish several structural properties, including explicit series representations, summation formulas, convolution identities, and recurrence relations involving the Golden derivative. Furthermore, we construct three-dimensional extensions and derive determinant representations for these polynomials. As special cases, we identify connections with Bernoulli-Fibonacci, Euler-Fibonacci, and Genocchi-Fibonacci polynomials. The results presented herein unify and extend several known Fibonacci-type polynomial families and provide a systematic Appell-type approach in Golden calculus.