A Note on Horadam Hybrinomials

Abstract

This paper ensures an extensive survey of the generalization of the various hybrid numbers and hybrid polynomials especially as part of its enhancing importance in the disciplines of mathematics and physics. In this paper, by using the Horadam polynomials, we define the Horadam hybrid polynomials called Horadam hybrinomials. We obtain some special cases and algebraic properties of the Horadam hybrinomials such as recurrence relation, generating function, exponential generating function, Binet formula, summation formulas, Catalan's identity, Cassini's identity and d'Ocagne's identity, respectively. Moreover, we give some applications related to the Horadam hybrinomials in matrices.

On the Generalized Gaussian Fibonacci Numbers and Horadam Hybrid Numbers: A Unified Approach

“…Finally, in [26], the author introduced the so-called Horadam hybrinomials. For n ≥ 1, the nth Horadam hybrinomial is defined by…”

Hyper-Leonardo Hybrinomials

“…Hybrid numbers have been the subject of much research recently [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Szynal-Liana and Wloch [16] defined the 𝑛-th Fibonacci hybrid number as…”

Hybrid hyper-Fibonacci and hyper-Lucas numbers

“…Cerda-Morales defined and studied the third-order Jacobsthal and modified third-order Jacobsthal hybrinomials in [7]. In [12], the author defined the new generalization of hybrinomial whose coefficients of basis are the Horadam polynomials and acquired some results of the Horadam hybrinomials.…”