HANKEL DETERMINANTS OF CERTAIN SEQUENCES OF BERNOULLI POLYNOMIALS: A DIRECT PROOF OF AN INVERSE MATRIX ENTRY FROM STATISTICS

被引：0

作者：

Jiu, Lin ^{[1
]}

Li, Ye ^{[2
]}

机构：

[1] Duke Kunshan Univ, Zu Chongzhi Ctr Math & Computat Sci, Suzhou 315216, Jiangsu, Peoples R China

[2] Duke Kunshan Univ, Class 2023, Suzhou 215316, Jiangsu, Peoples R China

来源：

CONTRIBUTIONS TO DISCRETE MATHEMATICS | 2024年 / 19卷 / 04期

关键词：

Hankel determinant; Bernoulli polynomial; Vandermonde matrix;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We calculate the Hankel determinants of certain sequences of Bernoulli polynomials. This corresponding Hankel matrix comes from statistically estimating the variance in nonparametric regression. Besides its entries' natural and deep connection with Bernoulli polynomials, a special case of the matrix can be constructed from a corresponding Vandermonde matrix. As a result, instead of asymptotic analysis, we give a direct proof of calculating an entry of its inverse. Further extensions also include an identity of Stirling numbers of both kinds.

引用

页码：64 / 84

页数：21