English

Hankel Determinants of shifted sequences of Bernoulli and Euler numbers

Number Theory 2021-05-06 v1

Abstract

Hankel determinants of sequences related to Bernoulli and Euler numbers have been studied before, and numerous identities are known. However, when a sequence is shifted by one unit, the situation often changes significantly. In this paper we use classical orthogonal polynomials and related methods to prove a general result concerning Hankel determinants for shifted sequences. We then apply this result to obtain new Hankel determinant evaluations for a total of 1313 sequences related to Bernoulli and Euler numbers, one of which concerns Euler polynomials.

Keywords

Cite

@article{arxiv.2105.01880,
  title  = {Hankel Determinants of shifted sequences of Bernoulli and Euler numbers},
  author = {Karl Dilcher and Lin Jiu},
  journal= {arXiv preprint arXiv:2105.01880},
  year   = {2021}
}