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On Generalized Fibospinomials: Generalized Fibonacci Polynomial Spinors
Version 1
: Received: 15 February 2024 / Approved: 16 February 2024 / Online: 16 February 2024 (14:15:45 CET)
How to cite: Colak, E. G.; Gonul Bilgin, N.; Soykan, Y. On Generalized Fibospinomials: Generalized Fibonacci Polynomial Spinors. Preprints 2024, 2024020910. https://doi.org/10.20944/preprints202402.0910.v1 Colak, E. G.; Gonul Bilgin, N.; Soykan, Y. On Generalized Fibospinomials: Generalized Fibonacci Polynomial Spinors. Preprints 2024, 2024020910. https://doi.org/10.20944/preprints202402.0910.v1
Abstract
In this paper, we introduce and investigate a new family of sequences called the generalized Fibospinomials (or the generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we handle with $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. After a short history on spinors and quaternions, we present Binet's formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some identities of generalized Fibonacci polynomial spinors, $(r,s)$-Fibonacci polynomial spinors and $(r,s)$-Lucas polynomial spinors. Moreover, we give some special identities such as Catalan's and Cassini's identities and we present matrices related with these polynomials.
Keywords
fibonacci numbers; fibonacci polynomials; fibonacci spinors; generalized fibonacci spinors; generalized fibonacci polynomial spinors
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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