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The paper proves the existence and elucidates the structure of the asymptotic expansion of the trace of the resolvent of a closed extension of a general elliptic cone operator on a compact manifold with boundary as the spectral parameter…

Analysis of PDEs · Mathematics 2023-10-24 Juan Gil , Thomas Krainer , Gerardo Mendoza

We study the large time behavior of solutions to the wave equation with space-dependent damping in an exterior domain. We show that if the damping is effective, then the solution is asymptotically expanded in terms of solutions of…

Analysis of PDEs · Mathematics 2024-03-12 Motohiro Sobajima , Yuta Wakasugi

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

Statistics Theory · Mathematics 2007-05-23 Teo Sharia

This paper establishes new results concerning asymptotic expansions of $q$-series related to partial theta functions. We first establish a new method to obtain asymptotic expansions using a result of Ono and Lovejoy, and then build on these…

Number Theory · Mathematics 2025-12-09 Alexander E. Patkowski

We consider operators acting in $L^2(\mathbb{R}^d)$ with $d\geq3$ that locally behave as a magnetic Schr\"odinger operator. For the magnetic Schr\"odinger operators we suppose the magnetic potentials are smooth and the electric potential is…

Spectral Theory · Mathematics 2024-09-10 Søren Mikkelsen

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…

Statistics Theory · Mathematics 2022-09-08 Yuliya Mishura , Hayate Yamagishi , Nakahiro Yoshida

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

We consider a class of pseudodifferential operators defined on the product of two closed manifolds, with crossed vector valued symbols. We study the asymptotic expansion of Weyl counting function of positive selfadjoint operators in this…

Spectral Theory · Mathematics 2012-01-13 Ubertino Battisti

We consider transcendental entire solutions of linear $q$-difference equations with polynomial coefficients and determine the asymptotic behavior of their Taylor coefficients. We use this to show that under a suitable hypothesis on the…

Complex Variables · Mathematics 2022-03-08 Walter Bergweiler

We combine the ideas of a Harish-Chandra--Howe local character expansion, which can be centred at an arbitrary semisimple element, and a Kim--Murnaghan asymptotic expansion, which so far has been considered only around the identity. We show…

Representation Theory · Mathematics 2019-02-20 Loren Spice

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 consider the asymptotic expansion of the sum \[S_p(a;w)=\sum_{n=1}^\infty n^{-w}\e^{-an^p}\] as $a\rightarrow 0$ in $|\arg\,a|<\pi/2$ for arbitrary finite $p>$ and $w>0$. Our attention is concentrated mainly on the case when $p$ and $w$…

Classical Analysis and ODEs · Mathematics 2015-03-26 R. B. Paris

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…

Number Theory · Mathematics 2024-11-13 Gergő Nemes

We consider a magnetic Schr\"odinger operator $H^h$, depending on the semiclassical parameter $h>0$, on a two-dimensional Riemannian manifold. We assume that there is no electric field. We suppose that the minimal value $b_0$ of the…

Spectral Theory · Mathematics 2010-01-12 Bernard Helffer , Yuri A. Kordyukov

We construct asymptotic expansions for the normalised incomplete gamma function $Q(a,z)=\Gamma(a,z)/\Gamma(a)$ that are valid in the transition regions, including the case $z\approx a$, and have simple polynomial coefficients. For Bessel…

Classical Analysis and ODEs · Mathematics 2019-03-26 Gergő Nemes , Adri B. Olde Daalhuis

Asymptotic approximations of Jacobi polynomials are given in terms of elementary functions for large degree $n$ and parameters $\alpha$ and $\beta$. From these new results, asymptotic expansions of the zeros are derived and methods are…

Classical Analysis and ODEs · Mathematics 2020-07-22 Amparo Gil , Javier Segura , Nico M. Temme

In this paper we study a semilinear elliptic problem on a bounded domain in $\R^2$ with large exponent in the nonlinear term. We consider positive solutions obtained by minimizing suitable functionals. We prove some asymtotic estimates…

Analysis of PDEs · Mathematics 2007-05-23 Khalil El Mehdi , Massimo Grossi

We study the asymptotic development at infinity of an integral operator. We use this development to give sufficient conditions in order to upper bound the number of critical periodic orbits that bifurcate from the outer boundary of the…

Dynamical Systems · Mathematics 2020-06-24 David Rojas

Asymptotic expansions are given for large values of $n$ of the generalized Bessel polynomials $Y_n^\mu(z)$. The analysis is based on integrals that follow from the generating functions of the polynomials. A new simple expansion is given…

Classical Analysis and ODEs · Mathematics 2011-01-26 José Luis López , Nico M. Temme

In this paper we present a complete asymptotic expansion of a symmetric homogeneous stable (balanced), stabilizable and stabilized mean. By including known asymptotic expansions of parametric means it is shown how the obtained coefficients…

Classical Analysis and ODEs · Mathematics 2024-07-15 Lenka Mihoković