A New Asymptotic Series and Estimates Related to Euler Mascheroni Constant
نویسندگان
چکیده
منابع مشابه
Inequalities for the Euler-Mascheroni constant
Let Rn = n k=1 1 k −log n + 1 2 , H(n) = n 2 (Rn −γ), n = 1, 2,. . ., where γ is the Euler-Mascheroni constant. We prove that for all integers n ≥ 1, H(n) and [(n + 1/2)/n] 2 H(n) are strictly increasing, while [(n + 1)/n] 2 H(n) is strictly decreasing. For all integers n ≥ 1, 1 24(n + a) 2 ≤ Rn − γ < 1 24(n + b) 2 with the best possible constants a = 1 24[−γ + 1 − log(3/2)] − 1 = 0.55106. .. a...
متن کاملLimits and inequalities associated with the Euler-Mascheroni constant
(i) We present several limits associated with the Euler-Mascheroni constant. (ii) Let γ = 0.577215 . . . be the Euler-Mascheroni constant, and let Tn = ∑n k=1 1 k − ln ( n+ 1 2 + 1 24n ) and Pn = ∑n k=1 2 2k−1 − ln(4n). We determine the best possible constants α, β, a and b such that the inequalities 1 48(n+ α)3 ≤ γ − Tn < 1 48(n+ β)3 and 1 24(n+ a)2 ≤ Pn − γ < 1 24(n+ b)2 are valid for all int...
متن کاملNew Fast Convergent Sequences of Euler-mascheroni Type
This sequence has diverse applications in many areas of mathematics, ranging from classical or numerical analysis to number theory, special functions or theory of probability. There is a huge literature about the sequence (γn)n≥1 and the constant γ. Please refer to [3, 4, 5, 6, 7, 8] and all the references therein. The speed of convergence to γ of sequence (γn)n≥1 is very slowly, if we take int...
متن کاملA new asymptotic expansion series for the constant pi
In our recent publications we have introduced the incomplete cosine expansion of the sinc function for efficient application in sampling [Abrarov & Quine, Appl. Math. Comput., 258 (2015) 425-435; Abrarov & Quine, J. Math. Research, 7 (2) (2015) 163-174]. Here we show that it can also be utilized as a flexible and efficient tool in mathematical analysis. In particular, an application of the inco...
متن کاملAsymptotic estimates for Apostol-Bernoulli and Apostol-Euler polynomials
We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials Bn(x;λ) in detail. The starting point is their Fourier series on [0, 1] which, it is shown, remains valid as an asymptotic expansion over compact subsets of the complex plane. This is used to determine explicit estimates on the constants in the approximation, and also to analyze oscillatory phenomena which arise in certain ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Constructive Mathematical Analysis
سال: 2020
ISSN: 2651-2939
DOI: 10.33205/cma.608927