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Best Lower and Upper Approximates to Irrational Numbers

✍ Scribed by Clark Kimberling

Publisher
Birkhäuser-Verlag
Year
1997
Weight
107 KB
Volume
52
Category
Article
ISSN
0013-6018

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📜 SIMILAR VOLUMES

The Best Approximation Function to Irrat
The Best Approximation Function to Irrational Numbers
✍ J.C. Tong 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 194 KB

Let \(\xi\) be an irrational number with simple continued fraction expansion \(\xi=\left[a_{0} ; a_{1}, a_{2}, \ldots, a_{i}, \ldots\right]\). Let the \(i\) th convergent \(p_{i} / q_{i}=\left[a_{0} ; a_{1}, a_{2}, \ldots, a_{i}\right]\). Let \(\mu=\) \(\left|\left[0 ; a_{n+2}, a_{n+3}, \ldots\right