一类广义的十次Freud-型权函数  

A Generalised Decic Freud-Type Weight

作　　者：王丹 朱孟坤 Yang Chen 王晓丽[2] Wang Dan;Zhu Mengkun;Yang Chen;Wang Xiaoli(Department of Mathematics,Faculty of Science and Technology,University of Macao,Avenida da Universidade,Macao Taipa 999078;School of Mathematics and Statistics,Qilu University of Technology(Shangdong Academy of Sciences),Jinan 250353)

机构地区：[1]澳门大学科技学院数学系,澳门999078 [2]齐鲁工业大学(山东省科学院)数学与统计学院,济南250353

出　　处：《数学物理学报（A辑）》2021年第4期921-935,共15页Acta Mathematica Scientia

基　　金：澳门科学技术发展基金(FDCT023/2017/A1);澳门大学基金(MYRG2018-00125FST);国家自然科学基金(11801292);广东省自然科学基金(2021A1515010361)。

摘　　要：该文构造了一类广义的十次Freud-型权函数w(x;t,α)=|x|~αe~(-x~(10)+tx~2),x,t∈■,α>-1研究了正交于该权函数的多项式的性质,得到其相关的循环系数β_n所满足的一系列差分-微分方程,并给出β_n的渐近行为.讨论并推导出关于该权函数的Hankel行列式在高维时(n→∞)满足的特性.最后,考虑了特殊情形下,即t=α=0时,由该权函数生成的Hankel矩阵的最小特征值问题.In this paper,the authors focus on a generalised decic Freud-type weight function w(x;t,a)=|x|αe-x10+tx2,t,x∈■,α>-1,and study the properties of the orthogonal polynomials with respect to this weight.The difference-differential equations of their associated recurrence coefficients are derived;meanwhile,the authors also find the asymptotic behavior of recurrence coefficients via above mentioned equations.What’s more,the authors discuss the Hankel determinant in regard to this weight as n→∞,and calculate the smallest eigenvalues of large Hankel matrices generated by this weight whenα=t=0.

关 键 词：正交多项式 循环系数 Hankel行列式 最小特征值 

分 类 号：O175.7[理学—数学]