Karl Dilcher, Lin Jiu
Published 2021-05-05Version 1
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.
Hankel determinants and Jacobi continued fractions for $q$-Euler numbers
Some new identities on the twisted (h, q)- Euler numbers and q-Bernstein polynomials
Note on q-extensions of Euler numbers and polynomials of higher order
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