Abstract
In this paper, we give a new process to study the convergence of periodic continued fractions, making use of the approach on the linear difference equations with periodic coefficients, based on the analytic formula of the linearly recurring sequences. Some new explicit expressions of nth numerators and nth denominators of the convergents of periodic continued fractions lead to discuss their convergence. Moreover, we provide a new discussion on the closed link between quadratic irrational numbers and simple periodic continued fractions. Some applications of the Pell’s equations are given and some numerical examples which illustrate the theory are supplied.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
