Related papers: Asymptotic zero behavior of Laguerre polynomials w…
In the paper, we propose two new conjectures about the convergence of Hermite Approximants of multivalued analytic functions of Laguerre class ${\mathscr L}$. The conjectures are based in part on the numerical experiments, made recently by…
Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be ``large.'' For a fixed $\alpha \in \Q - \Z_{<0}$, Filaseta and Lam have shown that the $n$th degree Generalized Laguerre…
In this paper, the structures to a family of biorthogonal polynomials that approximate to the Hermite and Generalized Laguerre polynomials are discussed respectively. Therefore, the asymptotic relation between several orthogonal polynomials…
We investigate multiple Charlier polynomials and in particular we will use the (nearest neighbor) recurrence relation to find the asymptotic behavior of the ratio of two multiple Charlier polynomials. This result is then used to obtain the…
We study the asymptotic behavior of Multiple Meixner polynomials of first and second kind, respectively (see J. Arves\'u et al. J. Comput. Appl. Math., 153, (2003)). We use an algebraic function formulation for the solution of the…
In this paper we consider sequences of polynomials orthogonal with respect to certain discrete Laguerre-Sobolev inner product, with two perturbations (involving derivatives) located inside the oscillatory region for the classical Laguerre…
We consider parameters $\lambda$ for which $0$ is preperiodic under the map $z\mapsto\lambda e^z$. Given $k$ and $l$, let $n(r)$ be the number of $\lambda$ satisfying $0<|\lambda|\leq r$ such that $0$ is mapped after $k$ iterations to a…
A two-parameter sequence of orthogonal polynomials $\{P_n( x; \lambda, t)\}_{n\ge 0}$ with respect to the weight function $x^\alpha e^{- \lambda x} \rho_\nu(x t),\ \alpha > -1,\ \lambda, t \ge 0, \ \rho_{\nu}(x)= 2 x^{\nu/2} K_\nu(2\sqrt…
We study the behavior of $r$-fold zeta-functions of Euler-Zagier type with identical arguments $\zeta_r(s,s,\ldots,s)$ on the real line. Our basic tool is an "infinite'' version of Newton's classical identities. We carry out numerical…
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…
Addressing a problem posed by W. Li and A. Wei (2009), we investigate the average number of (complex) zeros of a random harmonic polynomial $p(z) + \overline{q(z)}$ sampled from the Kac ensemble, i.e., where the coefficients are independent…
We establish an asymptotic formula for the logarithmic mean value of a 1-bounded multiplicative function that is sharp in many cases of interest. We derive from it a variety of applications, making progress on several old problems. As a…
We consider the orthogonal polynomials $\{P_{n}(z)\}$ with respect to the measure $|z-a|^{2N c} {\rm e}^{-N |z|^2} \,{\rm d} A(z)$ over the whole complex plane. We obtain the strong asymptotic of the orthogonal polynomials in the complex…
In this paper we consider generalized eigenvalue problems for a family of operators with a quadratic dependence on a complex parameter. Our model is $L(\lambda)=-\triangle +(P(x)-\lambda)^2$ in $L^2(\R^d)$ where $P$ is a positive elliptic…
In this paper we introduce spaces of $\textup{BLO}$-type related to Laguerre polynomial expansions. We consider the probability measure on $(0,\infty)$ defined by $d\gamma_\alpha(x)=\frac{2}{\Gamma(\alpha+1)}e^{-x^2}x^{2\alpha+1}dx$ with…
Following the work of Asai, Kaneko, and Ninomiya for Faber polynomials associated to $\mathrm{PSL}_2(\mathbb{Z})$, and Bannai, Kojima, and Miezaki's partial proof for the case of $\Gamma_0^*(2)$, we show that the zeros of certain modular…
We consider the orthogonal polynomials, $\{P_n(z)\}_{n=0,1,\cdots}$, with respect to the measure $$|z-a|^{2c} e^{-N|z|^2}dA(z)$$ supported over the whole complex plane, where $a>0$, $N>0$ and $c>-1$. We look at the scaling limit where $n$…
We analyze the eigenvalue density for the Laguerre and Jacobi $\beta$-ensembles in the cases that the corresponding exponents are extensive. In particular, we obtain the asymptotic expansion up to terms $o(1)$, in the large deviation regime…
New asymptotic relations between the $L_p$-errors of best approximation of univariate functions by algebraic polynomials and entire functions of exponential type are obtained for $p\in (0,\iy]$. General asymptotic relations are applied to…
In this article, we investigate the statistical distribution and asymptotic behavior of the family of monic integer polynomials of degree $n$ having at least one root in a fixed number field $K$. Although the framework of thin sets implies…