数学
拉盖尔多项式
递推关系
正交多项式
指数函数
库仑
操作员(生物学)
经典正交多项式
数学分析
组合数学
纯数学
物理
量子力学
电子
生物化学
化学
抑制因子
转录因子
基因
出处
期刊:Mathematics
[Multidisciplinary Digital Publishing Institute]
日期:2023-09-07
卷期号:11 (18): 3842-3842
被引量:1
摘要
In this paper, we consider the orthogonal polynomials with respect to the weight w(x)=w(x;s):=xλe−N[x+s(x3−x)],x∈R+, where λ>0, N>0 and 0≤s≤1. By using the ladder operator approach, we obtain a pair of second-order nonlinear difference equations and a pair of differential–difference equations satisfied by the recurrence coefficients αn(s) and βn(s). We also establish the relation between the associated Hankel determinant and the recurrence coefficients. From Dyson’s Coulomb fluid approach, we prove that the recurrence coefficients converge and the limits are derived explicitly when q:=n/N is fixed as n→∞.
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