Novel representations of log2 with polynomial continued fractions
Kadyrov S. Shynarbek N. Orynbassar A. Tahir M.A.
April 2026Springer Science and Business Media Deutschland GmbH
Arabian Journal of Mathematics
2026#15Issue 1247 - 254 pp.
This paper explores the representation of the mathematical constant log2 through polynomial continued fractions. Building upon prior work in continued fraction theory and recent advancements in automated conjectures for mathematical constants, we rigorously examine and extend a conjecture proposed by Zhu He (The Ramanujan Machine Project: Suggested new results by the community. https://www.ramanujanmachine.com/suggested-new-results-by-the-community/ (2020). Accessed 12 Mar 2025). The conjecture posits a specific polynomial continued fraction expansion for log2. We establish the validity of this conjecture and present an infinite family of new polynomial continued fractions for log2. Our results provide novel insights into the representation of log2 and contribute to the ongoing dialogue surrounding the precise characterization of mathematical constants using continued fractions.
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Department of General Education, New Uzbekistan University, Tashkent, Uzbekistan
Department of Pedagogy of Natural Sciences, SDU University, Kaskelen, Kazakhstan
School of Digital Technologies, Narxoz University, Almaty, Kazakhstan
Department of General Education
Department of Pedagogy of Natural Sciences
School of Digital Technologies
10 лет помогаем публиковать статьи Международный издатель
Книга Публикация научной статьи Волощук 2026 Book Publication of a scientific article 2026