Investigations about the Euler-Mascheroni constant and harmonic numbers (Q334532)
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scientific article; zbMATH DE number 6646245
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Investigations about the Euler-Mascheroni constant and harmonic numbers |
scientific article; zbMATH DE number 6646245 |
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Investigations about the Euler-Mascheroni constant and harmonic numbers (English)
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1 November 2016
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Euler-Mascheroni constant
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harmonic number
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digamma function
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rate of convergence
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The authors introduce a new sequence of real numbers which converges to the Euler-Mascheroni constant \(\gamma\), and determine a point where the given approximation is very fast. The results are then used to the improvement of certain known estimates on harmonic numbers.NEWLINENEWLINE Reviewer's remark: The authors seem not aware of a paper by the reviewer [C. R. Acad. Bulg. Sci. 41, No. 2, 19--21 (1988; Zbl 0667.34025)] where it is proved that, for any \(k\geq 3\), the integer part of \(H_m\) is \(k\), where \(m\) denotes the integer part of \(\exp(k-\gamma)+{1\over 2}\).
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