Year: 2025
Type: article
Abstract: The analytical study of the Pell number and the role of floor and ceiling functions into their computation is examined. Closed expressions of Pell numbers were initially derived using Binet's formula, followed by an asymptotic behavior study of the sequence using this formula. Taking into account the decreasing trend in the term $|\beta|^n = |1 - \sqrt{2}|^n$ for large values of $n$, a formula that closely approximates Pell numbers has been developed. In this context, relationships between numbers are clarified using floor and ceiling functions. The accuracy with which various theorems and lemmas mathematically prove these approximations is also included. The study also looks at limit processes with emphasis placed upon the determining influence that the ratio $\alpha = 1 + \sqrt{2}$ has on the growth rate of the sequence.
Authors: İsmail Sulan, Mustafa Aşçı
Institution: Pamukkale University
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4411006342