On an open problem of Chen and Mortici concerning the Euler–Mascheroni constant

Abstract

a b s t r a c t Chen and Mortici [Ch.-P. Chen, C. Mortici, New sequence converging towards the EulerMascheroni constant, Comput. Math. Appl. (2011); http://dx.doi.org/10.1016/j.camwa. 2011.03.099] proposed an open problem: for a given positive integer s, find the constantsis the fastest sequence which would converge to the Euler-Mascheroni constant γ . Using logarithmic type Bell polynomials, we solve this problem. The main result shows that the a i 's can be recursively determined.

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