论文标题
关于弗洛伊德型重量的某些特性：重新访问
On certain properties of perturbed Freud-type weight: a revisit
论文作者
论文摘要
在本文中，考虑了具有弗洛伊德型重量函数变形的一元多项式正交。这些多项式的全填充线性微分方程具有某些多项式系数，其全体形式。这项工作的目的是探索某些表征扰动的弗洛伊德型多项式的特性，例如非线性递归关系，有限的力矩，差异呈现和差异关系，以及相应的半经典正交多元元素所满足。我们注意到，所考虑的半经典多项式所实现的获得的微分方程用于研究基于stieltjes的原始思想的零分布的静电解释。
In this paper, monic polynomials orthogonal with deformation of the Freud-type weight function are considered. These polynomials fullfill linear differential equation with some polynomial coefficients in their holonomic form. The aim of this work is explore certain characterizing properties of perturbed Freud type polynomials such as nonlinear recursion relations, finite moments, differential-recurrence and differential relations satisfied by the recurrence coefficients as well as the corresponding semiclassical orthogonal polynomials. We note that the obtained differential equation fulfilled by the considered semiclassical polynomials are used to study an electrostatic interpretation for the distribution of zeros based on the original ideas of Stieltjes.
