Related papers: Combined fixed-order and effective-theory approach…

We evaluate in closed form series of the type $\sum u(n) R(n)$, where $(u(n))_n$ is a strongly $B$-multiplicative sequence and $R(n)$ a (well-chosen) rational function. A typical example is: $$ \sum_{n \geq 1} (-1)^{s_2(n)}…

We prove limit theorems for sums of randomly chosen random variables conditioned on the summands. We consider several versions of the corner growth setting, including specific cases of dependence amongst the summands and summands with heavy…

In acoustics, higher-order-in-time equations arise when taking into account a class of thermal relaxation laws in the modeling of sound wave propagation. In this work, we analyze initial boundary value problems for a family of such…

Infinite series sum_{n=1}^infty {(alpha/2)_n / (n n!)}_1F_1(-n, gamma, x^2), where_1F_1(-n, gamma, x^2)={n!_(gamma)_n}L_n^(gamma-1)(x^2), appear in the first-order perturbation correction for the wavefunction of the generalized spiked…

We derive the effective theories for heavy particles with a functional integral approach by integrating away the states with high velocity and with high virtuality. This formulation is non-perturbative and has a close connection with the…

Fast summation refers to a family of techniques for approximating $O(N^2)$ sums in $O(N\log{N})$ or $O(N)$ time. These techniques have traditionally found wide use in astrophysics and electrostatics in calculating the forces in a $N$-body…

When restricted to some non-negative multiplicative function, say f, bounded on primes and that vanishes on non square-free integers, our result provides us with an asymptotic for $\sum_{n \le X}f(n)/n$ with error term $O((\log…

We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…

The Erd\H{o}s-Ginzburg-Ziv theorem states that every sequence of 2n - 1 integers contains a subsequence of length n whose sum is divisible by n. Choi, Kang, and Lim gave a simple deterministic O(n log n) algorithm for finding such a…

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals

In this note we associate a sequence of non-negative integers to any convergent series of positive real numbers and study this sequence for the series $\sum_{n \geq 1} n^{-k}$ where $k$ is an integer $\geq 2$.

Generalized summability results are obtained regarding formal solutions of certain families of linear moment integro-differential equations with time variable coefficients. The main result leans on the knowledge of the behavior of the…

The well-known Bennett-Hoeffding bound for sums of independent random variables is refined, by taking into account truncated third moments, and at that also improved by using, instead of the class of all increasing exponential functions,…

In this paper, we prove coincidence and common fixed points results under nonlinear contractions on a metric space equipped with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially…

Considering the magnetic moment and polarizabilities of the nucleon we emphasize the need for relativistic chiral EFT calculations. Our relativistic calculations are done via the forward-Compton-scattering sum rules, thus ensuring the…

Temporal data, obtained in the setting where it is only possible to observe one time point per experiment, is widely used in different research fields, yet remains insufficiently addressed from the statistical point of view. Such data often…

We derive tests of stationarity for univariate time series by combining change-point tests sensitive to changes in the contemporary distribution with tests sensitive to changes in the serial dependence. The proposed approach relies on a…

We develop large sample theory for merged data from multiple sources. Main statistical issues treated in this paper are (1) the same unit potentially appears in multiple datasets from overlapping data sources, (2) duplicated items are not…

We show that the delta function potential can be exploited along with perturbation theory to yield the result of certain infinite series. The idea is that any exactly soluble potential if coupled with a delta function potential remains…

For $b>1$ and $\alpha\beta$ a string of two digits in base $b$, let $K_1$ be the subsum of the harmonic series with only those integers having exactly one occurrence of $\alpha\beta$. We obtain a theoretical representation of such $K_1$…