English
Related papers

Related papers: Explicit asymptotic expansions in p-adic harmonic …

200 papers

Hyperasymptotics is an analytical method that incorporates exponentially small contributions into asymptotic approximations, thereby expanding their domain of validity, improving accuracy, and providing deeper insight into the underlying…

Classical Analysis and ODEs · Mathematics 2026-02-17 Gergő Nemes

We are interested in the asymptotic behavior of orthogonal polynomials of the generalized Jacobi type as their degree $n$ goes to $\infty$. These are defined on the interval $[-1,1]$ with weight function…

Mathematical Software · Computer Science 2015-10-23 Alfredo Deaño , Daan Huybrechs , Peter Opsomer

Asymptotic expansions are derived for associated Legendre functions of degree $\nu$ and order $\mu$, where one or the other of the parameters is large. The expansions are uniformly valid for unbounded real and complex values of the argument…

Classical Analysis and ODEs · Mathematics 2025-07-04 T. M. Dunster

Parametric high-dimensional regression analysis requires the usage of regularization terms to get interpretable models. The respective estimators can be regarded as regularized M-functionals which are naturally highly nonlinear. We study…

Statistics Theory · Mathematics 2019-09-04 Tino Werner

In this paper, we introduce a notion of expansion for groupoids, which recovers the classical notion of expander graphs by a family of pair groupoids and expanding actions in measure by transformation groupoids. We also consider an…

Operator Algebras · Mathematics 2025-06-23 Xulong Lu , Qin Wang , Jiawen Zhang

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…

Classical Analysis and ODEs · Mathematics 2020-02-20 R B Paris

We study asymptotic expansion as $\nu\to0$ for integrals over ${ \mathbb{R} }^{2d}=\{(x,y)\}$ of quotients $F(x,y) \big/ \big( (x\cdot y)^2+(\nu \Gamma(x,y))^2\big)^{-1}$, where $\Gamma$ is strictly positive and $F$ decays at infinity…

Mathematical Physics · Physics 2018-01-17 Sergei Kuksin

We obtain an asymptotic expansion for $p(n)$, the number of partitions of a natural number $n$, starting from a formula that relates its generating function $f(t), t\in (0,1)$ with the characteristic functions of a family of sums of…

Number Theory · Mathematics 2019-08-21 Stella Brassesco , Arnaud Meyroneinc

Partial differential equations with highly oscillatory input terms are hardly ever solvable analytically and their numerical treatment is difficult. Modulated Fourier expansion used as an {\it ansatz} is a well known and extensively…

Numerical Analysis · Mathematics 2023-11-21 Karolina Kropielnicka , Rafał Perczyński

The aim of this article is to give a complete proof of results of Harish-Chandra linking the irreducibility of parabolic induction of a supercuspidal representation of a p-adic group to the analytic behavior of the mu-function of…

Representation Theory · Mathematics 2026-04-10 Volker Heiermann

First results towards a general method for asymptotic expansions of Feynman amplitudes in the loop-tree duality (LTD) formalism are presented. The asymptotic expansion takes place at integrand-level in the Euclidean space of the loop…

High Energy Physics - Phenomenology · Physics 2021-05-05 Judith Plenter , Germán Rodrigo

We establish precise asymptotic expansions for solutions to semilinear wave equations with power-type nonlinearities on asymptotically flat spacetimes. Our analysis focuses on two key cases: cubic nonlinearities and higher-order power…

Analysis of PDEs · Mathematics 2025-12-23 Shi-Zhuo Looi , Haoren Xiong

We define the ``lifted character'' of mod-$\ell$ representations of $p$-adic reductive groups where $\ell\not=p$, on compact elements with pro-orders not divisible by $\ell$. We generalize the local character expansion results of Howe,…

Representation Theory · Mathematics 2025-10-24 Cheng-Chiang Tsai

We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…

Probability · Mathematics 2007-05-23 Ph . Barbe , W. P. McCormick , C. Zhang

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…

High Energy Physics - Phenomenology · Physics 2009-10-30 M. Beneke , V. A. Smirnov

The cumulant representation of the Fourier path integral method is examined to determine the asymptotic convergence characteristics of the imaginary-time density matrix with respect to the number of path variables $N$ included. It is proved…

Computational Physics · Physics 2014-11-21 Sharif D. Kunikeev , David L. Freeman , J. D. Doll

In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic…

Analysis of PDEs · Mathematics 2014-01-28 Victor M. Calo , Yalchin Efendiev , Juan Galvis

In this paper, we use geometric tools to study the structure of asymptotic expanders and show that a sequence of asymptotic expanders always admits a "uniform exhaustion by expanders". It follows that asymptotic expanders cannot be coarsely…

Metric Geometry · Mathematics 2021-10-06 Ana Khukhro , Kang Li , Federico Vigolo , Jiawen Zhang

In this paper we refine an asymptotic expansion given by Soundararajan related to the Dickman function. The result suggests a relatively simple approach to computing these integrals numerically.

Number Theory · Mathematics 2018-11-13 C. S. Franze

We analytically compute asymptotic expansions of a 1-dimensional sub-manifold of stable and unstable manifolds in a 4-dimensional symplectic mapping by using the method called asymptotic expansions beyond all orders. This method enables us…

chao-dyn · Physics 2007-05-23 Yoshihiro Hirata , Tetsuro Konishi