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

[摘要] Chen and Mortici [Ch.-P. Chen, C. Mortici, New sequence converging towards the Euler-Mascheroni constant, Comput. Math. Appl. (2011); http://dx.doi.org/10.1016/j.camwa.2011.03.099] proposed an open problem: for a given positive integers, find the constants a(i)(i = 0, 1, 2,..., s) such that Sigma(n)(k=1) 1/k - log (n+Sigma(s)(i=0) a(i)n(-1)) is the fastest sequence which would converge to the Euler-Mascheroni constant gamma. Using logarithmic type Bell polynomials, we solve this problem. The main result shows that the a(i)'s can be recursively determined. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15

[关键词] Euler-Mascheroni constant;Bell polynomials;Logarithmic type Bell polynomials;Asymptotic expansion