On a new generalization of Fibonacci hybrid numbers

Tan, Elif; Ait-Amrane, N. Rosa

doi:10.1007/s13226-022-00264-3

Cited by 9 publications

(5 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Example 1. If n = 1 for Equation (19), n = 2 for Equation (20), and n = 0 for Equation (22) in Theorem 1, then we obtain…”

Section: Some New Results For Gaussian Leonardo Numbers and Related H...mentioning

confidence: 95%

See 1 more Smart Citation

On Gaussian Leonardo Hybrid Polynomials

Yağmur

2023

Symmetry

View full text Add to dashboard Cite

In the present paper, we first study the Gaussian Leonardo numbers and Gaussian Leonardo hybrid numbers. We give some new results for the Gaussian Leonardo numbers, including relations with the Gaussian Fibonacci and Gaussian Lucas numbers, and also give some new results for the Gaussian Leonardo hybrid numbers, including relations with the Gaussian Fibonacci and Gaussian Lucas hybrid numbers. For the proofs, we use the symmetric and antisymmetric properties of the Fibonacci and Lucas numbers. Then, we introduce the Gaussian Leonardo polynomials, which can be considered as a generalization of the Gaussian Leonardo numbers. After that, we introduce the Gaussian Leonardo hybrid polynomials, using the Gaussian Leonardo polynomials as coefficients instead of real numbers in hybrid numbers. Moreover, we obtain the recurrence relations, generating functions, Binet-like formulas, Vajda-like identities, Catalan-like identities, Cassini-like identities, and d’Ocagne-like identities for the Gaussian Leonardo polynomials and hybrid polynomials, respectively.

show abstract

“…Example 1. If n = 1 for Equation (19), n = 2 for Equation (20), and n = 0 for Equation (22) in Theorem 1, then we obtain…”

Section: Some New Results For Gaussian Leonardo Numbers and Related H...mentioning

confidence: 95%

“…Moreover, in Ref. [20], Tan and Ait-Amrane gave a generalization of Fibonacci and Lucas hybrid numbers and investigated some of their properties. Szynal-Liana and Wloch [21] introduced a new notion called the hybrinomials (alias hybrid polynomials).…”

Section: Respectivelymentioning

confidence: 99%

On Gaussian Leonardo Hybrid Polynomials

Yağmur

2023

Symmetry

View full text Add to dashboard Cite

show abstract

“…Polynomial versions of Fibonacci and Lucas hybrid numbers were studied in [27]. Tan and Ait-Amrane [28] introduced the bi-periodic Horadam hybrid numbers. Alp and Kocer [29] bring together hybrid numbers and Leonardo numbers and defined the hybrid Leonardo numbers as:…”

Section: Introductionmentioning

confidence: 99%

A New Class of Leonardo Hybrid Numbers and Some Remarks on Leonardo Quaternions over Finite Fields

Tan,

Savin,

Yılmaz

2023

Mathematics

Self Cite

View full text Add to dashboard Cite

In this paper, we present a new class of Leonardo hybrid numbers that incorporate quantum integers into their components. This advancement presents a broader generalization of the q-Leonardo hybrid numbers. We explore some fundamental properties associated with these numbers. Moreover, we study special Leonardo quaternions over finite fields. In particular, we determine the Leonardo quaternions that are zero divisors or invertible elements in the quaternion algebra over the finite field Zp for special values of prime integer p.

show abstract

“…In [8], the author considered the hybrid numbers with generalization of the Fibonacci numbers and acquired some results. The bi-periodic Horadam hybrid number was defined in [25]. In [11], Kizilates introduced the other new generalization of the hybrid number which called the 𝑞−Fibonacci hybrid numbers and the 𝑞−Lucas hybrid numbers and obtained some important algebraic properties of these numbers.…”

Section: Introductionmentioning

confidence: 99%

Hybrid hyper-Fibonacci and hyper-Lucas numbers

Alp¹

2023

NNTDM

View full text Add to dashboard Cite

Different number systems have been studied lately. Recently, many researchers have considered the hybrid numbers which are generalization of the complex, hyperbolic and dual number systems. In this paper, we define the hybrid hyper-Fibonacci and hyper-Lucas numbers. Furthermore, we obtain some algebraic properties of these numbers such as the recurrence relations, the generating functions, the Binet’s formulas, the summation formulas, the Catalan’s identity, the Cassini’s identity and the d’Ocagne’s identity.

show abstract

On a new generalization of Fibonacci hybrid numbers

Cited by 9 publications

References 10 publications

On Gaussian Leonardo Hybrid Polynomials

On Gaussian Leonardo Hybrid Polynomials

A New Class of Leonardo Hybrid Numbers and Some Remarks on Leonardo Quaternions over Finite Fields

Hybrid hyper-Fibonacci and hyper-Lucas numbers

Contact Info

Product

Resources

About