Related papers: Strong asymptotics for Jacobi polynomials with var…

We consider orthogonal polynomials $\{p_{n,N}(x)\}_{n=0}^{\infty}$ on the real line with respect to a weight $w(x)=e^{-NV(x)}$ and in particular the asymptotic behaviour of the coefficients $a_{n,N}$ and $b_{n,N}$ in the three term…

The exceptional $X_{1}$-Jacobi differential expression is a second-order ordinary differential expression with rational coefficients; it was discovered by G\'{o}mez-Ullate, Kamran and Milson in 2009. In their work, they showed that there is…

For random matrix ensembles with unitary symmetry, there is interest in the large $N$ form of the moments of the absolute value of the characteristic polynomial for their relevance to the Riemann zeta function on the critical line, and to…

Using the steepest descent method of Deift-Zhou, we derive locally uniform asymptotic formulas for the Meixner polynomials. These include an asymptotic formula in a neighborhood of the origin, a result which as far as we are aware has not…

We investigate the asymptotic behavior of the polynomials p, q, r of degrees n in type I Hermite-Pade approximation to the exponential function, defined by p(z)e^{-z}+q(z)+r(z)e^{z} = O(z^{3n+2}) as z -> 0. These polynomials are…

The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of asymptotically holomorphic extensions of $C^r$ ($r>3$)…

We study the classical problem of finding asymptotics for the Bessel functions $J_{\nu}(z)$ and $Y_{\nu}(z)$ as the argument $z$ and the order $\nu$ approach infinity. We use blow-up analysis to find asymptotics for the modulus and phase of…

We study the zero location and the asymptotic behavior of iterated integrals of polynomials. Borwein-Chen-Dilcher's polynomials play an important role in this issue. For these polynomials we find their strong asymptotics and give the limit…

We present a complete theory of the asymptotics of the zeros of OPUC with Verblunsky coefficients $\alpha_n = \sum_{\ell=1}^L C_\ell b_\ell^n + O((b\Delta)^n)$ where $\Delta <1$ and $\abs{b_\ell} = b<1$.

The eigenvalue correlations of random matrices from the Jacobi Unitary Ensemble have a known asymptotic behavior as their size tends to infinity. In the bulk of the spectrum the behavior is described in terms of the sine kernel, and at the…

In this paper, we study the Jacobi frame approximation with equispaced samples and derive an error estimation. We observe numerically that the approximation accuracy gradually decreases as the extended domain parameter $\gamma$ increases in…

Let W be an affine PI algebra over a field of characteristic zero graded by a finite group G. We show that there exist $\alpha_{1},\alpha_{2}\in\mathbb{R}, \beta\in\frac{1}{2}\mathbb{Z}$, and $l\in\mathbb{N}$ such that…

We study the leading order behaviour of positive solutions of the equation -\Delta u +\varepsilon u-|u|^{p-2}u+|u|^{q-2}u=0,\qquad x\in\R^N, where $N\ge 3$, $q>p>2$ and when $\varepsilon>0$ is a small parameter. We give a complete…

We derive semiclassical asymptotics for the orthogonal polynomials P_n(z) on the line with respect to the exponential weight \exp(-NV(z)), where V(z) is a double-well quartic polynomial, in the limit when n, N \to \infty. We assume that…

We provide necessary and sufficient conditions for a Jacobi matrix to produce orthogonal polynomials with Szeg\H{o} asymptotics off the real axis. A key idea is to prove the equivalence of Szeg\H{o} asymptotics and of Jost asymptotics for…

A method to obtain all-order asymptotic results for the coefficients of perturbative expansions in zero-dimensional quantum field is described. The focus is on the enumeration of the number of skeleton or primitive diagrams of a certain QFT…

Analytic combinatorics studies the asymptotic behaviour of sequences through the analytic properties of their generating functions. This article provides effective algorithms required for the study of analytic combinatorics in several…

Let $F$ be a non-degenerate quadratic form on an $n$-dimensional vector space $V$ over the rational numbers. One is interested in counting the number of zeros of the quadratic form whose coordinates are restricted in a smoothed box of size…

We prove asymptotic formulas for the complex coefficients of $(\zeta q;q)_\infty^{-1}$, where $\zeta$ is a root of unity, and apply our results to determine secondary terms in the asymptotics for $p(a,b,n)$, the number of integer partitions…

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…