Related papers: An Asymptotic relation for Hadjicostas Formula
We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give…
We discuss algebraic and combinatorial aspects of the Hamiltonian normal form theory. The main objective is to describe the normal form near a singular point purely in terms of the original Hamiltonian, avoiding the normalization procedure.…
Recent attempts at studying the Fermat equation over number fields have uncovered an unexpected and powerful connection with $S$-unit equations. In this expository paper we explain this connection and its implications for the asymptotic…
We establish some basic theorems in dimension theory and absolute extensor theory in the coarse category of metric spaces. Some of the statements in this category can be translated in general topology language by applying the Higson corona…
A concise and elementary derivation of the complete asymptotic expansion for the factorial function $n!$ is presented. This treatment produces a new expression for the coefficients, and it brings to light the simple relationship between the…
We present a formula describing the asymptotics of a class of multivariate orthogonal polynomials with hyperoctahedral symmetry as the degree tends to infinity. The polynomials under consideration are characterized by a factorized weight…
In this paper, we generalize the results of Evans and Tabrizian, by deriving asymptotics for the time-rescaled Kramers-Smoluchowski equations, in the case of a general non-symmetric potential function with multiple wells. The asymptotic…
We give an asymptotic equivalent at infinity of the unbounded solutions of some boundary layer equations arising in fluid mechanics.
We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[{}_2F_1(a+\epsilon\lambda,b;c+\lambda;x),\qquad 0<x<1\] as $\lambda\to+\infty$ in the neigbourhood of $\epsilon x=1$ when the parameter $\epsilon>1$ and…
An asymptotic formula for the number of partitions into p-cores is derived. As a byproduct some integer valued trigonometric sums are found
For a family of second-order parabolic systems with rapidly oscillating and time-dependent periodic coefficients, we investigate the asymptotic behavior of fundamental solutions and establish sharp estimates for the remainders.
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…
The classical Stirling's formula gives the asymptotic behavior of the gamma function. Katayama and Ohtsuki generalized this formula for Barnes' multiple gamma functions. In this paper, we further generalize these formulas for the multiple…
We propose a systematic method to derive the asymptotic behaviour of the persistence distribution, for a large class of stochastic processes described by a general Fokker-Planck equation in one dimension. Theoretical predictions are…
We consider general subordination and obtain the formula of the subordinated predictable compensator. An example of application is given.
We study some properties concerning the asymptotic behavior of solutions to nonautonomous retarded functional differential equations, depending on the knowledge of certain solutions of the associated generalized characteristic equation.
This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…
The asymptotic expansion of $n$-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explicit formula for the action of these…
We present several results that show somewhat surprising equidistribution patterns in the asymptotic behaviour of the argument of entire functions of finite order.
t is proved in this paper that there is a fine correlation between the values of $|\zeta(1/2+i\varphi(t)/2)|^4$ and $|\zeta(1/2+it)|^2$ which correspond to two segments with gigantic distance each from other. This new asymptotic formula…