On the rational approximations to \(\tanh{1\over k}\). II (Q1805022)
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scientific article; zbMATH DE number 751378
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the rational approximations to \(\tanh{1\over k}\). II |
scientific article; zbMATH DE number 751378 |
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On the rational approximations to \(\tanh{1\over k}\). II (English)
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10 April 1996
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Let \(k\) be any positive integer. In part I [ibid. 69, No. 6, 161-163 (1993; Zbl 0806.11032)]\ the author had proved (among other things) that for arbitrary \(\varepsilon> 0\) there are infinitely many solutions in reduced fractions \(p/q\) of the inequality \[ |\tanh (1/k)- p/q|< (1/ (2k)+ \varepsilon) (\log \log q)/ (q^2 \log q). \] He now improves this by showing that in fact \(\varepsilon\) can be taken to be zero. The complete version has been published in Tokyo J. Math. 18, No. 1, 75- 80 (1995) see below.
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