Hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas Quaternions with it’s associated Spinor algebra

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Document Type : Original paper

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Department of Mathematics, Central University of Jharkhand, India

Abstract

In this article, we introduce and study hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas spinors. First, we give hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas quaternions with some algebraic properties. Next we introduce the spinor family of $k$-Mersenne and $k$-Mersenne-Lucas numbers using the hyperbolic $k$-Mersenne and $k$-Mersenne-Lucas quaternions. Here, we start with Binet-type formulas and algebraic properties such as Catalan's identity, Cassini's identity, d'Ocagne's identity, etc. Additionally, we obtain various types of generating functions. Moreover, we give partial sum formulas in closed form.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 03 September 2024

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