Moreover, asymptotic expressions of the finite sums of powers of binomial coefficients for these numbers are given. Some numeric values of these asymptotic expressions are illustrated by the tables. Finally, some inequalities for these numbers are given.KILAR, NESLIHAN...
The following sections are included:PreliminariesOrders of magnitudeRiemann sumsPermanence principlesMass and tail of a random variableAsymptotic properties of the binomial coefficientsExercisesdoi:10.1142/9789812779229_0002IMME van den BERGWorld Scientific Publishing Co. Pte. Ltd....
-convergence, an asymptotic description of the algorithm in the limit of infinitely fine partition cells. the limit trajectory of couplings is described by a continuity equation on the product space where the momentum is purely horizontal and driven by the gradient of the cost function. global opti...
These congruences can hold modulo arbitrarily large powers of $p$. Unlike results for finite multiple zeta values, weighted congruences typically involve harmonic sums of multiple weights, which are multiplied by explicit powers of $p$ depending on weight. We also introduce certain formal weighted ...
On minimal asymptotic basis of order g−1 2019, Indagationes Mathematicae Show abstract Let g⩾3 be an integer. Let A be the set of all nonempty finite sums of distinct powers of g and all numbers of the form 2⋅gr with r⩾0. In this paper, we construct an asymptotic basis ...
An important application of Slutky's theorem relates to statistics that can be decomposed as a sum of terms for which some CLT holds plus a term that converges in probability to 0. Assume, for example, that the variables Yi have a finite fourth central moment γ and write the sample varia...
The framework of trans-Planckian asymptotic safety has been shown to generate phenomenological predictions in the Standard Model and in some of its simple
We study Daugavet- and-points in Banach spaces. A norm one elementxis a Daugavet-point (respectively, a-point) if in every slice of the unit ball (respectively, in every slice of the unit ball containingx) you can find another element of distance as close to 2 fromxas desired. In ...
Finite-Part Integrals And The Euler-Maclaurin Expansion The context of this note is the discretization error made by the m -panel trapezoidal rule when the integrand has an algebraic singularity at one end, say ... Lyness,J.N - Birkhäuser Boston 被引量: 53发表: 1994年 加载更多引用...
Using Euler —Maclaurin summation formula, we get the general re sults for asymptotic estimations of finite sums. 本文利用Euler— Maclaurin求和公式得到了有限和渐近估计的一般结果,作为特 例,改进和推广了华罗庚[1]的两个有广泛应用的定理,还给出了某些有趣的应用。