Related papers: Asymptotics of some generalized Mathieu series

For the Chebyshev-Stirling numbers, a special case of the Jacobi-Stirling numbers, asymptotic formulae are derived in terms of a local central limit theorem. The underlying probabilistic approach also applies to the classical Stirling…

We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one. We also give an application of natural boundaries in determining asymptotic results.

For the Legendre-Stirling numbers of the second kind asymptotic formulae are derived in terms of a local central limit theorem. Thereby, supplements of the recently published asymptotic analysis of the Chebyshev-Stirling numbers are…

Using a recently derived integral in terms of elementary functions, we derive new asymptotic expansions of the normal inverse Gaussian cumulative distribution function. One of the asymptotic representations is in terms of the normal…

A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…

We prove that the (suitably rescaled) moments of certain discrete measures on the unit interval, which are related to the numerical evaluation of zeta series with missing digits in radix $b$, are asymptotically $1$-periodic in the base $b$…

Asymptotic expansions are given for large values of $n$ of the generalized Bernoulli polynomials $B_n^\mu(z)$ and Euler polynomials $E_n^\mu(z)$. In a previous paper L\'opez and Temme (1999) these polynomials have been considered for large…

We improve existing estimates of moments of the Riemann zeta function. As a consequence, we are able to derive new estimates for the asymptotic behaviour of $\sum_{N \alpha \le x} \mathfrak{t}_k(\alpha)$, where $N$ stands for the norm of a…

The paper solves the problems of determining the asymptotics of the number of primes and the sums of functions of primes in a subset of the natural series that satisfies the conditions that the asymptotic density of the number of primes in…

Given a sequence of complex square matrices, $a_n$, consider the sequence of their partial products, defined by $p_n=p_{n-1}a_{n}$. What can be said about the asymptotics as $n\to\infty$ of the sequence $f(p_n)$, where $f$ is a continuous…

The article is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second order elliptic…

We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous…

The resummation of superfactorially divergent series represents a significant computational challenge in mathematical physics. In the present paper the resummation of a specific class of Stieltjes series characterized by a moment sequence…

This paper delves on the versatility of the theory of Khinchin families for asymptotic estimation. We show that in combination with Local Central Limit theorems for lattice variables, Khinchin families furnish a convenient and unified…

We address the problem of ambiguity of a function determined by an asymptotic perturbation expansion. Using a modified form of the Watson lemma recently proved elsewhere, we discuss a large class of functions determined by the same…

Using the steepest descent method of Deift-Zhou, we derive locally uniform asymptotic formulas for the Meixner polynomials. These include an asymptotic formula in a neighborhood of the origin, a result which as far as we are aware has not…

For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…

We consider the three conjectures stated in a 2003 paper of Wu, concerning the asymptotics of particular sums of products of binomials, powers and logarithms. These sums relate to the form of the regularised integrals used in loop…

The paper establishes the central limit theorems and proposes how to perform valid inference in factor models. We consider a setting where many counties/regions/assets are observed for many time periods, and when estimation of a global…

We analyze the asymptotic behavior of the Apostol-Bernoulli polynomials $\mathcal{B}_{n}(x;\lambda)$ in detail. The starting point is their Fourier series on $[0,1]$ which, it is shown, remains valid as an asymptotic expansion over compact…