β-连分数的渐近分数
The Convergent in Continued β-Fraction
DOI: 10.12677/AAM.2018.712192, PDF,   
作者: 肖 倩：华南理工大学，广东 广州
关键词: β-连分数；渐近分数；收敛；Continued β-Fraction； Convergent； Converges
摘要: 设β=(√5+1)/2，T为[0,1)上的β-连分数变换，Pn(x)/qn(x)是x的n阶β-渐近分数。本文证明了序列(Pn(x)/qn(x))n ≥1的一些性质，并且证明了(Pn(x)/qn(x))n ≥1收敛且收敛到x。
Abstract: Let (√5+1)/2, T is the continued β-fraction transformation on [0,1), and Pn(x)/qn(x) is the nth-order β-fraction-convergent of x. In this paper, we show many properties of the sequence (Pn(x)/qn(x))n ≥1. Moreover, we prove that (Pn(x)/qn(x))n ≥1 converges to x.
文章引用：肖倩. β-连分数的渐近分数[J]. 应用数学进展, 2018, 7(12): 1645-1649. https://doi.org/10.12677/AAM.2018.712192

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