Hurwitz连分数中误差和函数的若干性质
Some Properties of the Error-Sum Function of Hurwitz Continued Fractions
DOI: 10.12677/pm.2025.154110, PDF,    科研立项经费支持
作者: 曹子昂, 罗 玉, 沈陆明*：湖南农业大学信息与智能科学技术学院，湖南 长沙
关键词: Hurwitz连分数；误差和函数；正则连分数；图像维数；Hurwitz Continued Fractions； Error-Sum Function； Regular Continued Fractions； Graph Dimension
摘要: 对各类展式的误差和函数的研究从21世纪初就开始了，研究人员不断深入探讨其各种性质，如连续性、周期性、有界性、介值性等，同时给出函数图像的Hausdorff维数。在本文中，我们将探讨Hurwitz连分数的误差和函数，提出一些相关的性质，并研究其图像。
Abstract: The study of error-sum functions of expansions has been ongoing since the beginning of the 21st century, and researchers have been delving into various properties such as continuity, periodicity, boundedness, median, etc., along with giving the Hausdorff dimension of the graphs of the functions. In this paper, we will explore the error-sum function of Hurwitz continued fractions, present some related properties, and study their graphs.
文章引用：曹子昂, 罗玉, 沈陆明. Hurwitz连分数中误差和函数的若干性质[J]. 理论数学, 2025, 15(4): 68-75. https://doi.org/10.12677/pm.2025.154110

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