On 3-parameter quaternions with higher order generalized Fibonacci numbers components

Kızılateş, Can; Kibar, İsmail Yusuf

doi:10.1007/s41478-024-00730-7

Cited by 2 publications

(1 citation statement)

References 24 publications

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“…1 (γ) = 1. For γ = 1, the higher-order generalized Fibonacci polynomial U (s) n (γ) becomes the higher-order generalized Fibonacci numbers studied by Kızılateş and Kibar [7]. These polynomials have the following algebraic properties as follows:…”

Section: Introductionmentioning

confidence: 99%

On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations

Kızılateş,

Du,

Terzioğlu

2024

Mathematics

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This paper presents a comprehensive survey of the generalization of hybrid numbers and hybrid polynomials, particularly in the fields of mathematics and physics. In this paper, by using higher-order generalized Fibonacci polynomials, we introduce higher-order generalized Fibonacci hybrid polynomials called higher-order generalized Fibonacci hybrinomials. We obtain some special cases and algebraic properties of the higher-order generalized Fibonacci hybrinomials, such as the recurrence relation, generating function, exponential generating function, Binet formula, Vajda’s identity, Catalan’s identity, Cassini’s identity and d’Ocagne’s identity. We also present three different matrices whose components are higher-order generalized Fibonacci hybrinomials, higher-order generalized Fibonacci polynomials and Lucas polynomials. By using these matrices, we obtain some identities related to these newly established hybrinomials.

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Section: Introductionmentioning

confidence: 99%

On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations

Kızılateş,

Du,

Terzioğlu

2024

Mathematics

Self Cite

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New Properties and Matrix Representations on Higher-Order Generalized Fibonacci Quaternions with q-Integer Components

Kızılateş,

Du,

Terzioğlu

et al. 2024

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In this paper, by using q-integers and higher-order generalized Fibonacci numbers, we define the higher-order generalized Fibonacci quaternions with q-integer components. We give some special cases of these newly established quaternions. This article examines q-calculus and quaternions together. We obtain a Binet-like formula, some new identities, a generating function, a recurrence relation, an exponential generating function, and sum properties of quaternions with quantum integer coefficients. In addition, we obtain some new identities for these types of quaternions by using three new special matrices.

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On 3-parameter quaternions with higher order generalized Fibonacci numbers components

Cited by 2 publications

References 24 publications

On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations

On Higher-Order Generalized Fibonacci Hybrinomials: New Properties, Recurrence Relations and Matrix Representations

New Properties and Matrix Representations on Higher-Order Generalized Fibonacci Quaternions with q-Integer Components

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