Fast convergences towards 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…”

Section: Introductionmentioning

confidence: 99%

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

Yang

2012

Journal of Mathematical Analysis and Applications

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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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“…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 ).…”

Section: A Without Channel Estimation Energy (E T = 0)mentioning

confidence: 99%

“…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…”

Section: B With Channel Estimation Energy (E T = 0)mentioning

confidence: 99%

Opportunistic Wireless Energy Transfer in Point-to-Point Links

Thudugalage

Atapattu

Evans

2019

2019 IEEE Wireless Communications and Networking Conference (WCNC)

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In this paper we consider wireless energy transfer for a point-to-point link. The energy transmitter sees a finite number of independent channel realizations, and, armed with (causal) knowledge of the channels, must decide how much energy to transmit in each time slot. The objective is to maximize the expected energy transferred to the receiver at the end of the time period. We show that the optimal energy allocation policy is binary: the transmitter sends no energy or all energy in a slot with this decision based on a simple threshold on the channel. As intuition demands, this threshold for transmission decreases as we move closer to the last available time slot. The performance of the optimal scheme is studied both analytically and numerically.Index Terms-Channel estimation, single-input single-output (SISO) network, threshold policy, wireless energy transfer.

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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.

Cited by 30 publications

References 26 publications

Some best approximation formulas and inequalities for the Wallis ratio

Some best approximation formulas and inequalities for the Wallis ratio

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

Opportunistic Wireless Energy Transfer in Point-to-Point Links

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