Properties of generalized Freud polynomials
Properties of generalized Freud polynomials
复制标题
DOI：
10.1016/j.jat.2017.10.001
复制
发表时间：
2016-06
期刊：
影响因子：
--
通讯作者：
P. Clarkson;K. Jordaan
中科院分区：
文献类型：
--
作者：
P. Clarkson;K. Jordaan
我们考虑半经典广义Freud权函数w λ（x; t）=| X| 2 λ+ 1 exp（− x 4+ t x 2），λ>− 1，x∈ R.我们分析了关于w λ（x; t）正交的一元多项式序列的渐近行为，以及当次数或参数t趋于无穷大时递归系数的渐近行为。研究了递推系数所满足的非线性离散方程正解的存在唯一性，证明了广义Freud多项式零点的性质.
We consider the semiclassical generalized Freud weight function w λ (x; t)=| x| 2 λ+ 1 exp (− x 4+ t x 2), λ>− 1, x∈ R. We analyse the asymptotic behaviour of the sequences of monic polynomials that are orthogonal with respect to w λ (x; t), as well as the asymptotic behaviour of the recurrence coefficient, when the degree, or alternatively, the parameter t, tend to infinity. We also investigate existence and uniqueness of positive solutions of the nonlinear discrete equation satisfied by the recurrence coefficients and prove properties of the zeros of the generalized Freud polynomials.