An S-fraction and \(\ell n^ 2(1+x)\) (Q1122037)
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scientific article; zbMATH DE number 4105349
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An S-fraction and \(\ell n^ 2(1+x)\) |
scientific article; zbMATH DE number 4105349 |
Statements
An S-fraction and \(\ell n^ 2(1+x)\) (English)
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1989
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\(\ell n^ 2(1+x)=\frac{1|}{| y}+\frac{-p_ 1q_ 1|}{| 1}+\frac{-p_ 2q_ 2|}{| y}+...\), where \( y=(1-x)/x^ 2,\quad p_{2s}+q_{2s-1}=0\), \(q_{2s+1}+q_{2s}=1\) \((s=1,2,...)\). This implies \(\ell n^ 2(1+x)<x^ 2/(1+x)\) and more complicated upper and lower bounds valid for \(x>-1\).
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continued fractions
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logarithm
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S-fraction
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inequalities
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