Hankel Determinants of shifted sequences of Bernoulli and Euler numbers

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 t...

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Bibliographic Details
Published in:Contributions to discrete mathematics 2023-01, Vol.18 (2), p.146-175
Main Authors: Dilcher, Karl, Jiu, Lin
Format: Article
Language:English
Online Access:Get full text
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Summary: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.
ISSN:1715-0868
1715-0868
DOI:10.55016/ojs/cdm.v18i2.73995