euler's constant, sequences and some estimates
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euler's constant, sequences and some estimates

;Alina Sîntămărian
journal of oral pathology & medicine : official publication of the international association of oral pathologists and the american academy of oral pathology 2013 Vol. 8 (2013) pp. 103-114
150
sntmrian2013surveyseuler's

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.

Keywords

sequence convergence estimatemathematics

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