Fast convergences towards Euler-Mascheroni constant

Abstract

Abstract. The aim of this paper is to introduce a new family of sequences which faster converge to the Euler-Mascheroni constant. Finally, numerical computations are given.Mathematical subject classification: 41A60, 41A25, 57Q55.

Some best approximation formulas and inequalities for the Wallis ratio

“…Remark 2.1. Lemma 2.1 was first established in [15] and has been effectively applied in many papers such as [2,3,6,7,8,9,10,11,13,14,16].…”

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

“…Later, some faster approximations to the Euler-Mascheroni constant were established in [3][4][5][6]. For example, Negoi [6] proved that the sequence…”

Opportunistic Wireless Energy Transfer in Point-to-Point Links

“…where γ is the Euler-Mascheroni constant (γ = 0.5772...) [18]. Proof: Define a sequence U N as U N = ∆ N j=0 c j −ln(N ).…”

“…Step: Consider the case N = n+1. The optimization problem in (18) can be written as By using the threshold policy assumption, we have two cases: i) ρ n = e t for |h n | 2 < γ n (P ) which leads to s n−1 = 1; and ii) ρ n = P for |h n | 2 > γ n (P ) which leads to s n−1 = 0, where γ n (P ) is the threshold at frame n. Thus, the objective function of (23) can be given as…”