A generalization of Euler's constant (Q2464636)

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A generalization of Euler's constant
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    A generalization of Euler's constant (English)
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    17 December 2007
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    As a generalization of the Euler's constant \(\gamma\), the author considers the series \[ \gamma(a)= \lim_{n\rightarrow\infty} \sum_{i=1}^n 1/(a+i-1)- \ln((a+n-1)/a) \quad\text{for }a>0; \] first she proves that \(\gamma(a)\) is a decreasing function of \(a\) and then she gives some related sequences, comparable by \(\gamma(a)\) and useful to evaluate it. Reviewer's remark: As I know, there are various generalizations of the Euler's constant. For example, see \textit{J. Sondow} and \textit{P. Hadjicostas}, J. Math. Anal. Appl. 332, No. 1, 292--314 (2007; Zbl 1113.11017) and \textit{M. Spreafico}, Funkts. Anal. Prilozh. 39, No. 2, 87--91 (2005; Zbl 1115.33002).
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    Euler's constant
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    inequality
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    series
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