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On the bicomplex Fibonacci $p$ quaternions | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، Special Issue- Dedicated to the memory of Jürgen Herzog (1941-2024).، تیر 2026، صفحه 217-233 اصل مقاله (147.09 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2026.27743.1682 | ||
| نویسنده | ||
| B. Prasad* | ||
| Department of Mathematics, Kandi Raj College, Kandi, India | ||
| چکیده | ||
| The paper introduces a novel bicomplex Fibonacci p quaternions, establishing algebraic properties, Honsberger identity, D’Ocagne’s identity, Cassini’s identity, Catalan’s identity for these quaternions. The study extends previous work on bicomplex Fibonacci quaternions [10] by incorporating bicomplex Fibonacci p quaternions. These new quaternions may have implications in applied mathematics, quantum mechanics, quantum physics, Lie groups, Kinematics and differential equations. | ||
| کلیدواژهها | ||
| Fibonacci numbers؛ Golden mean؛ Bicomplex quaternions؛ Bicomplex Fibonacci quaternions | ||
| مراجع | ||
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1] F. T. Aydin, Bicomplex Fibonacci quaternions, Chaos, Solitons and Fractals, 106 (2018), 147-153. [2] M. Basu and B. Prasad, The generalized relations among the code elements for Fibonacci coding theory, Chaos, Solitons and Fractals, 41 (2009), 2517-2525. [3] M. Basu and B. Prasad, Long range variations on the Fibonacci universal code, Journal of Number Theory, 130 (2010), 1925-1931. [4] C. Celemoglu, On bicomplex (p, q) Fibonacci quaternions, Chaos, Mathematics, 12 (2024), 461(18 pages). [5] O. Diskaya and H. Menken, On the Pseudo-Fibonacci and Pseudo-Lucas Quaternions, Electronic Journal of Mathematical Analysis and Applications, (1) 12 (2024), 1-9. [6] M. S. EL Naschie, Topics in the mathematical physics of e-infinity theory, Chaos, Solitons and Fractals, 30 (2006), 656-663. [7] M. S. EL Naschie, The theory of cantorian space time and high energy particle physics, Chaos, Solitons and Fractals, 41 (2009), 2635-2646. [8] W. R. Hamilton, Elements of Quaternions, London, Longmans, Green and Company, 1866. [9] A. F. Horadam, Complex Fibonacci numbers and Fibonacci quaternions, Am Math Month, (3) 70 (1963), 289-291. [10] B. Prasad, The generalized relations among the code elements for a new complex Fibonacci matrix, Discrete Mathematics Algorithms and Applications, (2) 11 (2019), 1950026 (16 pages). [11] A. P. Stakhov, Fibonacci matrices, a generalization of the cassini formula and a new coding theory, Chaos, Solitons and Fractals, 30 (2006), 56-66. [12] A. P. Stakhov, The golden matrices and a new kind of cryptography, Chaos, Solitons and Fractals, 32 (2007), 1138-1146. | ||
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