On a generalization of Euler constant in connection to di-Gamma function

Abstract

In this paper we study the sequences {xn}, {yn} defined for each n ≥ 1 by ... , in connection to Gamma and di-Gamma function. Our results generalize some previous ones in [Berinde, V. A new generalization of Euler’s constant, Creat. Math.Inform. 18 (2009), No. 2, 123–128] and [Sant ˆ am˘ arian, A., ˘ A generalization of Euler constant, Mediamira, Cluj-Napoca, 2008] and are inspired from the paper [Mortici, C., Improved convergence towards generalized Euler-Mascheroni constant, Appl. Math. Comput., 2009, doi: 10.1016/j.amc.2009.10.039].