Related papers: Explicit asymptotic expansions in p-adic harmonic …
Analytic solutions and their formal asymptotic expansions for a family of the singularly perturbed $q-$difference-differential equations in the complex domain are constructed. They stand for a $q-$analog of the singularly perturbed partial…
The purpose of this article is to study the asymptotic expansion of Ray-Singer analytic tosion associated with increasing powers p of a given positive line bundle. Here we prove that the asymptotic expansion associated to a manifold…
We give two algorithms that allow to get arbitrary precision asymptotics for the harmonic potential of a random walk.
We develop the theory of a new type of asymptotic expansions for functions of two variables the coefficients of which contain functions of one of the variables as well as functions of the quotient of these two variables. These combined…
We develop the theory of a new type of asymptotic expansions for functions of two variables the coefficients of which contain functions of one of the variables as well as functions of the quotient of these two variables. These combined…
Fermi-Dirac integrals appear in problems in nuclear astrophysics, solid state physics or in the fundamental theory of semiconductor modeling, among others areas of application. In this paper, we give new and complete asymptotic expansions…
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…
We consider the asymptotic expansion of Kr\"atzel's integral \[F_{p,\nu}(x)=\int_0^\infty t^{\nu-1} e^{-t^p-x/t}\,dt\qquad (|\arg\,x|<\pi/2),\] for $p>0$ as $|x|\to \infty$ in the sector $|\arg\,x|<\pi/2$ employing the method of steepest…
In a previous article of the authors with M. Canalis-Durand, monomial asymptotic expansions, Gevrey asymptotic expansions and monomial summability were introduced and applied to certain systems of singularly perturbed differential…
Computer algebra algorithms are developed for evaluating the coefficients in Airy-type asymptotic expansions that are obtained from integrals with a large parameter. The coefficients are defined from recursive schemes obtained from…
When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.
Let $\rm E/\rm F$ be an unramified quadratic extension of local non archimedean fields of characteristic 0. Let $\underline{H}$ be an algebraic reductive group, defined and split over $\rm F$. We assume that the split connected component of…
We consider the asymptotic expansion of the functional series \[S_{\mu,\gamma}(a;\lambda)=\sum_{n=1}^\infty \frac{n^\gamma e^{-\lambda n^2/a^2}}{(n^2+a^2)^\mu}\] for real values of the parameters $\gamma$, $\lambda>0$ and $\mu\geq0$ as…
One discusses a problem of asymptotical behavior for some operators in a general theory of pseudo differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit representations for these…
We established and estimate the full asymptotic expansion in integer powers of 1 N of the [ $\sqrt$ N ] first marginals of N-body evolutions lying in a general paradigm containing Kac models and non-relativistic quantum evolution. We prove…
We derive a complete asymptotic expansion of generalized Witten integrals for Hamiltonian circle actions on arbitrary symplectic manifolds, characterizing the coefficients in the expansion as integrals over the symplectic strata of the…
Given an observable and its operator product expansion (OPE), we present expressions that carefully disentangle truncated sums of the perturbative series in powers of $\alpha$ from the non-perturbative (NP) corrections. This splitting is…
We construct a new type of convergent asymptotic representations, dyadic factorial expansions. Their convergence is geometric and the region of convergence can include Stokes rays, and often extends down to 0^+. For special functions such…
We derive high-order terms in the asymptotic expansions of the steady-state voltage potentials in the presence of a finite number of diametrically small inhomogeneities with conductivities different from the background conductivity. Our…
In this paper, we derive new results on the asymptotic behavior of eigenvalues of perturbed one-dimensional massive Dirac operators in the weak coupling limit. Two classes of potentials are considered. For bounded Hermitian potentials $V$…