Related papers: Asymptotic behavior of summation functions from bo…

We present an asymptotic evaluation unitary formula for large argument values existing for defined class of functions. The asymptotic evaluation is obtained using only power series expansion coefficients of a function, what is a new result…

In a paper in the American Mathematical Monthly, the corresponding author asks for an asymptotic of a gcd-sum function \begin{align}\sum_{ab\leq N}\tau(\gcd(a,b))\label{eqn:taugcdsum}\end{align} We extensively study generalizations of the…

The paper considers the properties of pseudo stationarity in a broad sense and pseudo strong mixing for sequences of random variables corresponding to arithmetic functions. Assertions on this topic have been proven. The implementation of…

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 $p$…

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…

Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…

We give asymptotic analysis of power series associated with lacunary partition functions. New partition theoretic interpretations of some basic hypergeometric series are offered as examples.

In this document, we make a round up of the theory of asymptotic normality of sums of associated random variables, in a coherent approach in view of further contributions for new researchers in the field. (Version 01)

We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures.

The asymptotic behavior of the mean values of multiple zeta functions is of significant interest due to its close connection with the Riemann zeta function. In this paper, we establish asymptotic behavior of the mean square values of Barnes…

In this paper we give an improvement of the degree of the homogeneous linear recurrence with integer coefficients that exponential sums of symmetric Boolean functions satisfy. This improvement is tight. We also compute the asymptotic…

The paper compares the asymptotic of the expressions $\frac {1} {x} \sum\limits_{n \leq x} {f(n)}$ and $\sum\limits_{n \leq x} {\frac {f(n)} {n}}$, $\frac {1} {x} \sum\limits_{p \leq x} {f(p)}$ and $\sum\limits_{p \leq x} {\frac {f(p)}…

This note contains some asymptotic formulas for the sums of various residue classes of Euler's phi-function.

We present several results that show somewhat surprising equidistribution patterns in the asymptotic behaviour of the argument of entire functions of finite order.

The aim of this paper is to give, using some contiguous relations, the asymptotic behaviour of some linear combination of two symmetric contiguous hypergeometric functions, under some conditions of their parameters.

In this paper, we investigate the asymptotics of a class of weighted sums over multiplicative functions and apply our results to deduce a stronger asymptotic form of Yitang Zhang's smoothened GPY sieve with coefficient expressions that are…

The paper proves a generalization of Wintner's theorem on the asymptotics of summation functions to the case of summation functions with nonlinear asymptotics. The class of arithmetic functions that have a logarithmic asymptotic mean is…

We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…

This paper concerns the estimation of sums of functions of observable and unobservable variables. Lower bounds for the asymptotic variance and a convolution theorem are derived in general finite- and infinite-dimensional models. An explicit…

Let $p$ be a prime number, $k\ge 0$ and $f$ be a class of arithmetic functions satisfying some simple conditions. In this short paper, we study the asymptotical behaviour of summation function $$\psi_{f,k}(x):=\sum_{n\le x}\Lambda…