Dual-complex generalized k-Horadam numbers

Year 2021, Volume: 70 Issue: 1, 117 - 129, 30.06.2021

Sure Köme Cahit Köme Yasin Yazlik

https://doi.org/10.31801/cfsuasmas.780861

Cited By: 1

Abstract

The purpose of this paper is to provide a broad overview of the generalization of the various dual-complex number sequences, especially in the disciplines of mathematics and physics. By the help of dual numbers and dual-complex numbers, in this paper, we define the dual-complex generalized k-Horadam numbers. Furthermore, we investigate the Binet formula, generating function, some conjugation identities, summation formula and a theorem which is generalization of the Catalan's identity, Cassini's identity and d'Ocagne's identity.

Keywords

Dual Numbers, Dual-Complex Numbers, Generalized k-Horadam Numbers, Dual-Complex Generalized k-Horadam Numbers

References

• Aydın, F. T., Dual−complex k−Fibonacci numbers, Chaos, Solitons & Fractals, 115 (2018), 1–6.
• Aydın, F. T., Dual−complex k−Pell quaternions, arXiv preprint arXiv:1810.05002 (2018).
• Brodsky, V., Shoham, M., Dual numbers representation of rigid body dynamics, Mechanism and machine theory, 34 (5) (1999), 693–718.
• Clifford, W. K., A preliminary sketch of biquaternions, 1873.
• Dimentberg, F. M., The screw calculus and its applications in mechanics, Foreign Technology Division, 1969.
• Falcon, S., On the k−Lucas numbers, International Journal of Contemporary Mathematical Sciences, 6 (21) (2011), 1039–1050.
• Falcón, S., Plaza, Á., The k−Fibonacci sequence and the pascal 2-triangle, Chaos, Solitons & Fractals, 33 (1) (2007), 38-49.
• Fischer, I., Dual−number methods in kinematics, statics and dynamics, Routledge, 2017.
• Fjelstad, P., Gal, S. G., n−dimensional dual complex numbers, Advances in Applied Clifford Algebras, 8 (2) (1998), 309–322.
• Güngör, M. A., Azak, A. Z., Investigation of dual-complex fibonacci, dual-complex lucas numbers and their properties, Advances in Applied Clifford Algebras, 27 (4) (2017), 3083– 3096.
• Horadam, A., A generalized Fibonacci sequence, The American Mathematical Monthly, 68 (5) (1961), 455–459.
• Horadam, A., Special properties of the sequence w n (a, b; p, q), The Fibonacci Quarterly, 5 (5) (1967), 424–434.
• Horadam, A., et al., Generating functions for powers of a certain generalised sequence of numbers, Duke Mathematical Journal, 32 (3) (1965), 437–446.
• Irmak, N., More identities for Fibonacci and Lucas quaternions, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 69 (1) (2020), 369–375.
• Koshy, T., Fibonacci and Lucas numbers with applications. 2001, A Wiley-Interscience Publication.
• Liu, L., On the spectrum and spectral norms of r−circulant matrices with generalized k−Horadam numbers entries, International Journal of Computational Mathematics, 2014 (2014).
• Majernik, V., Multicomponent number systems, Acta Physica. Polonica A., 90 (3) (1996), 491–498.
• Matsuda, G., Kaji, S., Ochiai, H., Anti-commutative dual complex numbers and 2d rigid transformation, In Mathematical Progress in Expressive Image Synthesis I, Springer, 2014, pp. 131–138.
• Messelmi, F., Dual-complex numbers and their holomorphic functions.
• Study, E., Geometrie der dynamen, 1903, Study, E., Geometrie der dynamen, 1903.
• Tan, E., Leung, H.-H., Some results on Horadam quaternions, Chaos, Solitons & Fractals, 138 (2020), 109961.
• Yazlik, Y., Köme, C., Madhusudanan, V., A new generalization of Fibonacci and Lucas p−numbers, Journal of Computational Analysis and Applications, 25 (4) (2018), 657–669.
• Yazlik, Y., Köme, S., Köme, C., Bicomplex generalized k−Horadam quaternions, Miskolc Mathematical Notes, 20 (2) (2019), 1315–1330.
• Yazlik, Y., Taskara, N., A note on generalized k−Horadam sequence, Computers & Mathematics with Applications, 63 (1) (2012), 36–41.