Hankel Determinants of shifted sequences of Bernoulli and Euler numbers
DOI:
https://doi.org/10.55016/ojs/cdm.v18i2.73995Abstract
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 14 sequences related to Bernoulli and Euler numbers, one of which concerns Euler polynomials.
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