Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 8 (2013), 103 -- 114

EULER'S CONSTANT, SEQUENCES AND SOME ESTIMATES

Alina Sîntămărian

Abstract. We give a class of sequences with the argument of the logarithmic term modified and that converge quickly to a generalization of Euler's constant denoted by γ(a), i.e. the limit of the sequence (∑k=1n1/(a+k-1)-ln((a+n-1)/a)n∈ℕ, where a∈(0,+∞).
Also, we obtain estimates for γ-(∑k=1n1/k-ln(n+1/2+1/(24(n+1/2)))), where γ=γ(1) is the Euler's constant.

2010 Mathematics Subject Classification: 11Y60; 11B68; 40A05; 41A44; 33B15.
Keywords: Sequence; Convergence; Approximation; Euler's constant; Bernoulli number; Estimate.

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Alina Sîntămărian
Department of Mathematics,
Technical University of Cluj-Napoca,
Str. Memorandumului nr. 28,
400114 Cluj-Napoca,
Romania.
e-mail: Alina.Sintamarian@math.utcluj.ro

http://www.utgjiu.ro/math/sma