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On the harmonic number expansion by Ramanujan
2013
Journal of Inequalities and Applications
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Let γ = 0.577215664 . . . denote the Euler-Mascheroni constant, and let the sequences The main aim of this paper is to find the values r, s, t, a, b, c and d which provide the fastest sequences (u n ) n≥1 and (v n ) n≥1 approximating the Euler-Mascheroni constant. Also, we give the upper and lower bounds for n k=1 1 k -1 2 ln(n 2 + n + 1 3 ) -γ in terms of n 2 + n + 1 3 . MSC: 11Y60; 40A05; 33B15
doi:10.1186/1029-242x-2013-222
fatcat:lra27yjfgzc7nogv7vurrn75ta