This paper explores the representation of the mathematical constant \(\log 2\) 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 \(\log 2\) . We establish the validity of this conjecture and present an infinite family of new polynomial continued fractions for \(\log 2\) . Our results provide novel insights into the representation of \(\log 2\) and contribute to the ongoing dialogue surrounding the precise characterization of mathematical constants using continued fractions.
