Research article
On Bivariate Fubini-Fibonacci Polynomials and Numbers
Abstract
In this paper, we introduce a new type of Fubini polynomials called bivariate Fubini-Fibonacci polynomials, denoted by \(F_{n}^{f}(x, y)\) using golden exponential function, via generating function\[\frac{e_{f}^{xt}}{1-y(e_{f}^{t}-1)}=\sum_{n=0}^{\infty} F_{n}^{f}(x,y) \frac{t^{n}}{f_{n}!}. \nonumber\]We then derive some fundamental properties of these polynomials including addition formula, explicit formula, recurrence relations, and derivative and integral formulas. Moreover, we establish the relationships between Fubini-Fibonacci polynomials and other Fibonacci polynomials and obtain the harmonic-based \(f\)-exponential generating functions of Fubini-Fibonacci polynomials and numbers.
How to cite
N. C. Ampaso, N. G. Acala, On Bivariate Fubini-Fibonacci Polynomials and Numbers, Pan-Amer. J. Math. 5 (2026), 5. https://doi.org/10.28919/cpr-pajm/5-5
BibTeX
@article{Ampaso2026,
author = {Ampaso, Normia C. and Acala, Nestor G.},
title = {On Bivariate Fubini-Fibonacci Polynomials and Numbers},
journal = {Pan-Amer. J. Math.},
volume = {5},
year = {2026},
pages = {5},
doi = {10.28919/cpr-pajm/5-5}
}