Leading coefficient in the Hankel determinants related to binomial and $q$-binomial transforms
Number Theory
2024-01-31 v1 Combinatorics
Abstract
It is a standard result that the Hankel determinants for a sequence stay invariant after performing the binomial transform on this sequence. In this work, we extend the scenario to -binomial transforms and study the behavior of the leading coefficient in such Hankel determinants. We also investigate the leading coefficient in the Hankel determinants for even-indexed Bernoulli polynomials with recourse to a curious binomial transform. In particular, the degrees of these Hankel determinants share the same nature as those in one of the -binomial cases.
Keywords
Cite
@article{arxiv.2401.17220,
title = {Leading coefficient in the Hankel determinants related to binomial and $q$-binomial transforms},
author = {Shane Chern and Lin Jiu and Shuhan Li and Liuquan Wang},
journal= {arXiv preprint arXiv:2401.17220},
year = {2024}
}