Related papers: A note on an asymptotic expansion related to the D…

We present an asymptotic expansion for a family of multiple integrals connected with relatives of the Dickman function. The coefficients of this expansion have a similar arithmetic structure as those appearing in work of Soundararajan on an…

We prove a conjecture of Broadurst (arXiv:1004.0519v1) on asymptotic expansions of certain polylogarithm type functions related to the Dickman function.

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…

Integral means are important class of bivariate means. In this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean. It is based on explicit solving the equation of the form…

In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.

We present expressions for the coefficients which arise in asymptotic expansions of multiple integrals of Laplace type (the first term of which is known as Laplace's approximation) in terms of asymptotic series of the functions in the…

In this paper, insight is given in the techniques used to compute asymptotic expansions. In a broad fashion the technique is described. Most of the results apply to the paper "An expansion for the maximum likelihood estimator and its…

In this paper, by using asymptotic expansions of oscillatory integrals with positive real power phase functions in one variable, we obtain asymptotic expansions of oscillatory integrals with phase functions expressed by a product of…

We consider the asymptotic expansion of the generalised exponential integral involving the Mittag-Leffler function introduced recently by Mainardi and Masina [{\it Fract. Calc. Appl. Anal.} {\bf 21} (2018) 1156--1169]. We extend the…

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.…

Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…

We present general prescriptions for the asymptotic expansion of massive multi-loop Feynman integrals near threshold. As in the case of previously known prescriptions for various limits of momenta and masses, the terms of the threshold…

This article is focused on the asymptotic expansions, as time tends to infinity, of solutions of a system of ordinary differential equations with non-smooth nonlinear terms. The forcing function decays to zero in a very complicated but…

In the past few years we have derived asymptotic expansions for lambda_d of the dimer problem and lambda_d(p) of the monomer-dimer problem. The many expansions so far computed are collected herein. We shine a light on results in two…

In [Temme N.M., Special functions. An introduction to the classical functions of mathematical physics, A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York, 1996, Section 11.3.3.1] a uniform asymptotic expansion for the…

General results on asymptotic expansions of Feynman diagrams in momenta and/or masses are reviewed. It is shown how they are applied for calculation of massive diagrams.

Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. For this, a recently developed theory of asymptotic expansion of the distribution of Wiener functionals is applied. The effects of…

In this paper, under certain restrictions on linear factors of the denominator of a rational function of two variables, the leading term of the asymptotic expansion of the coefficients is found.

We provide several asymptotic expansions of the prime counting function $\pi(x)$ and related functions. We define an {\it asymptotic continued fraction expansion} of a complex-valued function of a real or complex variable to be a possibly…

Recently, there has been renewed interest in studying the asymptotic properties of the integer partition function $p(n)$. Hardy, Ramanujan, and Rademacher provided detailed asymptotic analysis for $p(n)$. Presently, attention has shifted…