Explicit, determinantal, recursive formulas, and generating functions of generalized Humbert-Hermite polynomials via generalized Fibonacci polynomials
Can Kizilates
article (Uluslararası, Hakemli) | Yazar(lar): Can Kizilates | Yıl: 2023 | Dergi/Kurum: MATHEMATICAL METHODS IN THE APPLIED SCIENCES | İndeks: WOS.SCI | DOI: 10.1002/mma.9048 | Anahtar Kelimeler: Fibonacci polynomials, generalized Fibonacci polynomials, generating function, Hessenberg determinant, Humbert-Hermite polyno
In this paper, using the Faa di Bruno formula and some properties of the Bell polynomials of the second kind, we obtain a new explicit formula for the generalized Humbert-Hermite polynomials. We provide determinantal representations for the ratio of two differentiable functions. We obtain a recursive relation for the generalized Humbert-Hermite polynomials. As a practice, we derive an alternative recursive relation for generalized Humbert-Hermite polynomials via the Hessenberg determinant. Finally, we derive several families of multilinear and multilateral generating functions for the generalized Humbert-Hermite-type polynomials and other polynomials which are mentioned in this paper. Our results also include many well-known polynomials in the literature.