相关论文: On the function sum(-k^2/s^2)
In this paper, we introduce the notion of $\psi$-quadratic $k$-tuples. We also give examples, prove some properties and propose generalizations of these new concepts.
The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice non-trivial (non-Gaussian) fluctuations of the measured…
Some properties of the inverse of the Normal distribution are studied. Its derivatives, integrals and asymptotic behavior are presented.
When we have two expansions of physical quantity around two different points in parameter space, we can usually construct a family of functions, which interpolates the both expansions. In this paper we study analytic structures of such…
Explicit analytic expressions are derived for the effective-range function for the case when the interaction is represented by a sum of the short-range square-well and long-range Coulomb potentials. These expressions are then transformed…
Threshold expansions of the $\pi\pi$ and $K\overline{K}$ spin 0 and isospin 0 scattering amplitudes are performed. Scattering lengths, effective ranges and so--called volume parameters are evaluated. Good agreement with the existing…
A mathematical procedure is suggested to obtain deformed entropy formulas of type K(S_K) = sum_i P_i K(-ln P_i), by requiring zero mutual K(S_K)-information between a finite subsystem and a finite reservoir. The use of this method is first…
The main result of the paper is the Fibonacci-like property of the partition function. The partition function $p(n)$ has a property: $p(n) \leq p(n-1) + p(n-2)$. Our result shows that if we impose certain restrictions on the partition, then…
We extend the insertion approach for calculating depletion potentials to the case of non-spherical solutes. Instead of a brute-force calculation we suggest to employ the recently developed curvature expansion of density profiles close to…
We examine the sum of modified Bessel functions with argument depending non-linearly on the summation index given by \[S_{\nu,p}(a)=\sum_{n\geq 1} (an^p/2)^{-\nu} K_\nu(an^p)\qquad (a>0,\ 0\leq\nu<1)\] as the parameter $a\to 0+$, where $p$…
The sum $c_0(1/k)=-\sum_{m=1}^{k-1}(m/k)\cot(m{\pi}/k)$ is related to the Estermann zeta function. A recent paper computes the first two terms of the large-$k$ asymptotic expansion of $c_0(1/k)$. Using the Poisson summation formula for…
In this note we discuss solutions of differential equation $(D^2-\alpha^2)^{k}u=0$ on $\mathbb{R}\setminus\mathbb{Z}$, which we call hyperbolic splines. We develop the fundamental function of interpolation and prove various properties…
This technical note describes the application of saddle-point integration to the asymptotic Fourier analysis of the well-known $C_\infty$ "bump" function $\exp[-(1-x^2)^{-1}]$, deriving both the asymptotic decay rate $k^{-3/4} \exp(-\sqrt…
We introduce an analytic function $\Psi(s_1,\ldots,s_r;w)$ that interpolates truncated multiple zeta functions $\zeta_N(s_1,\ldots,s_r)$. We represent this interpolant as a Mellin transform of a function $G(q_1,\ldots,q_r;w)$ and, using…
The sum of proper divisors function $s(n)$ has been studied for more than 2000 years. In this paper we study statistical properties of the related function $S_s(n) := \sum_{d \mid n} s(d)$. This function arises from a generalization of the…
In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration.
We study the convexity of the entropy functional along particular interpolating curves defined on the space of finitely supported probability measures on a graph.
We generalize the asymptotic estimates by Bubboloni, Luca and Spiga (2012) on the number of $k$-compositions of $n$ satisfying some coprimality conditions. We substantially refine the error term concerning the number of $k$-compositions of…
A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground state density of a given system. Then, the…
In this paper we establish a new summation method by expanding $\prod_{k}(1-\frac{z}{a_{k}})^{-1}$ with two approaches: the Taylor expansion and the infinite partial fraction decomposition. Here we focus on the case when $a_{k}$ is…