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2023•Journal of Engineering Technology and Applied SciencesOpen access

Hybrinomials Related to Hyper-Fibonacci and Hyper-Lucas Numbers

Efruz Özlem MERSİN

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Abstract

Hybrid number system is a generalization of complex, hyperbolic and dual numbers. Hybrid numbers and hybrid polynomials have been the subject of much research in recent years. In this paper, hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers are defined. Then some algebraic properties of newly defined hybrinomials are examined such as the recurrence relations and summation formulas. Also, the relation between hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers is given. Additionally, hybrid hyper-Fibonacci and hybrid hyper-Lucas numbers are defined by using the hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers.

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What this paper is about

Hybrid number system is a generalization of complex, hyperbolic and dual numbers. Hybrid numbers and hybrid polynomials have been the subject of much research in recent years. In this paper, hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers are defined. Then some algebraic properties of newly defined hybrinomials are examined such as the recurrence relations and summation formulas. Also, the relation between hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers is given. Additionally, hybrid hyper-Fibonacci and hybrid hyper-Lucas numbers are defined by using the hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers.

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Available abstract

Hybrid number system is a generalization of complex, hyperbolic and dual numbers. Hybrid numbers and hybrid polynomials have been the subject of much research in recent years. In this paper, hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers are defined. Then some algebraic properties of newly defined hybrinomials are examined such as the recurrence relations and summation formulas. Also, the relation between hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers is given. Additionally, hybrid hyper-Fibonacci and hybrid hyper-Lucas numbers are defined by using the hybrinomials related to hyper-Fibonacci and hyper-Lucas numbers.

Key concepts: Lucas number, Fibonacci number, Fibonacci polynomials, Lucas sequence, Pisano period, Recurrence relation, Mathematics, Generalization

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