Related papers: Asymptotic behavior of summation functions from bo…
We present here a large collection of harmonic and quadratic harmonic sums, that can be useful in applied questions, e.g., probabilistic ones. We find closed-form formulae, that we were not able to locate in the literature.
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
We consider a sum of the derivatives of Dirichlet $L$-functions over the zeros of Dirichlet $L$-functions. We give an asymptotic formula for the sum.
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
In this paper, we study the asymptotic behavior of supremum distribution of some classes of iterated stochastic processes $\{X(Y(t)) : t \in [0, \infty)\}$, where $\{X(t) : t \in \mathbb{R} \}$ is a centered Gaussian process and $\{Y(t): t…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…
Using recent results from the theory of integer points close to smooth curves, we give an asymptotic formula for the distribution of values of a class of integer-valued prime-independent multiplicative functions.
In this paper, we establish the existence of large solutions of Hessian equations and obtain a new boundary asymptotic behavior of solutions.
Our aim in this report is to investigate the asymptotic behavior of Mittag-Leffler functions. We give some estimates involving the Mittag-Leffler functions and their derivatives.
We study the asymptotic behavior of homeomorphic solutions of the Beltrami equation with different conditions on the dilatation at infinity in this paper.
In this paper, we study sums of shifted products $\sum\limits_{n \leq x} F(n) G(n-h)$ for any $|h| \leq x/2$ and arithmetic functions $F=f*1$ and $G=g*1$, with $f$ and $g$ small. We obtain asymptotic formula for different orders of…
Regular and singular parts of asymptotic expansions of semi-Markov random evolutions are given. Regularity of boundary conditions is shown. An algorithm for calculation of initial conditions is proposed.
It was believed that the Mertens function is a simple random walk in the first versions of the article, so its asymptotic behavior obeys the law of the iterated logarithm. In the latest version of the article we show why the asymptotic…
In this paper we improve a result on the order of magnitude of certain cotangent sums associated to the Estermann and the Riemann zeta functions.
The work is devoted to the construction of the asymptotic behavior of the solution of a singularly perturbed system of equations of parabolic type, in the case when the limit equation has a regular singularity as the small parameter tends…
In this work we study the asymptotics of the fractional Laplacian as $s\to 0^+$ on any complete Riemannian manifold $(M,g)$, both of finite and infinite volume. Surprisingly enough, when $M$ is not stochastically complete this asymptotics…
The paper explores various special functions which generalize the two-parametric Mittag-Leffler type function of two variables. Integral representations for these functions in different domains of variation of arguments for certain values…
In this paper we extend a result on the asymptotics of moments of certain cotangent sums associated to the Estermann and Riemann zeta functions established in a previous paper for integer exponents to arbitrary positive real exponents.
A compilation of new results on the asymptotic behaviour of the Humbert functions $\Psi_1$ and $\Psi_2$, and also on the Appell function $F_2$, is presented. As a by-product, we confirm a conjectured limit which appeared recently in the…
In this paper, we introduce the hypermultiple gamma functions of BM-type and prove the asymptotic expansion of these functions.