Hankel Determinants of shifted sequences of Bernoulli and Euler numbers

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 $13$ sequences related to Bernoulli and Euler numbers, one of which concerns Euler polynomials.