arXiv:2109.00772 Abstract | arXiv Analytics

arXiv:2109.00772 [math.NT]Abstract References Reviews Resources

Hankel Determinants of Certain Sequences Of Bernoulli Polynomials: A Direct Proof of an Inverse Matrix Entry from Statistics

Published 2021-09-02Version 1

We calculate the Hankel determinants of 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.

Categories: math.NT, math.CO, math.ST, stat.TH

Subjects: 11B68, 05A19, 11B73, 15A15

Keywords: bernoulli polynomials, inverse matrix entry, hankel determinants, direct proof, statistics

Related articles: Most relevant | Search more

arXiv:0709.2593 [math.NT] (Published 2007-09-17)

Symmetric identities on Bernoulli polynomials

Amy M. Fu, Hao Pan, Fan Zhang

arXiv:1206.3826 [math.NT] (Published 2012-06-18, updated 2013-09-02)

On the integral of the product of four and more Bernoulli polynomials

Su Hu, Daeyeoul Kim, Min-Soo Kim

arXiv:2005.03874 [math.NT] (Published 2020-05-08)

On Alzer-Kwong's Identities for Bernoulli polynomials