On the convergence of periodic continued fractions via linearly recurring sequences
*R. Ben TaherCorresponding authorbentaher89@hotmail.frDepartment of MathematicsFaculty of SciencesMoulay Ismail University, B.P. 4010Beni M’hamed, Meknès, MoroccoView full profile → , D. Zioualziouald@gmail.comDepartment of MathematicsFaculty of SciencesMoulay Ismail University, B.P. 4010Beni M’hamed, Meknès, MoroccoView full profile → , H. Benkhaldounbenkhaldoun.hajar@gmail.comDepartment of MathematicsFaculty of SciencesMoulay Ismail University, B.P. 4010Beni M’hamed, Meknès, MoroccoView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 12 Jul 2022
- Published Online:
- 07 May 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-1728
- Pages:
- 497–510
Abstract
Keywords
Subject Classifications
References
[1] R. Ben Taher, H.Benkhaldoun, Solving the linear difference equation with periodic coefficients via Fibonacci sequences, Linear and Multilinear Algebra. 67, 2549-2564 (2019). https://doi.org/10.1080/03081087.2018.1497584.
[2] R. Ben Taher, H. Benkhaldoun, M. Rachidi, On some class of periodic-discrete homogeneous difference equations via Fibonacci sequences, Journal of Difference Equations and Applications 22, 1292-1306 (2016). http://doi.org/10.1080/10236198.2016.1194407.
[3] R. Ben Taher, and M. Rachidi, On the matrix powers and exponential by r-generalized Fibonacci sequences methods: the companion matrix case, Linear Algebra and Its Applications 370, 341-353 (2003). DOI: 10.1016/S0024-3795(03)00418-X.
[4] S. Hyun Yang, Continued Fractions and Pell’s Equation, University of Chicago REU Papers. (2008).
[5] S. Kadyrov and F. Mashurov. Generalized continued fraction expansions for and e, Journal of Discrete Mathematical Sciences and Cryptography, 24:6, 1809-1819 (2021), DOI: 10.1080/09720529.2021.1936897.
[6] M. Mouline, M. Rachidi, Application of Markov chains properties to r-generalized Fibonacci sequences, Fibonacci Quart. 37, 34-38 (1999).
[7] J.-M. Muller, Elementary Functions: Algorithms and Implementation, 3rd edition, Birkhäuser Boston, MA (2016).
[8] P. Ngo. Exact Comparison of Quadratic Irrationals. [Research Report] LIGM. (2011). URL: https://hal.archives-ouvertes.fr/hal-00691762 (accessed on 30 September 2021).
[9] C.D. Olds, Continued Fractions, From the New Mathematical Library, Random House (1963).
[10] K. Rosen. Elementary Number theory and its applications. 3rd edition. Addison-Wesley, Reading (1992).
[11] R. Seidensticker, Continued fractions for high-speed and high-accuracy computer arithmetic, Proceedings of the 6th Symposium on Computer Arithmetic, 184-193 (1983).
