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Let γ = 0.577215664 . . . denote the Euler-Mascheroni constant, and let the sequences {equation presented}. 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 (vn)n≥1 approximating the Euler-Mascheroni constant. Also, we give the upper and lower bounds for{equation presented} - γ in terms of n2 + n + 13. © 2013 Mortici and Chen; licensee Springer.

On the harmonic number expansion by Ramanujan