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Partial Results on Hankel Determinants and the Corresponding J-Fractions of a Sequence Related to Bernoulli Numbers
Abstract
When exploring the Hankel determinant of the sequence μk=Bk+1/(k+1), where Bk is the k-th Bernoulli number, we obtained two interesting results. The first one applies in general to all sequences (ck)k≥0 with all even-indexed term $0$, except for c0. In this case, the coefficient of the second highest order of the corresponding monic orthogonal polynomials determines the Hankel determinants. Our second result shows, the corresponding J-fractions, obtained from the generating function of μk, is exactly the same as in early work of Cao, on a faster sequence converging to the Euler--Mascheroni constant.
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BibTeX
@misc{jiu2026partial,
title = {{Partial Results on Hankel Determinants and the Corresponding J-Fractions of a Sequence Related to Bernoulli Numbers}},
author = {Lin Jiu and Yihang Yin},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05827},
eprint = {2609.05827},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05827},
}
RIS
TY - UNPB
TI - Partial Results on Hankel Determinants and the Corresponding J-Fractions of a Sequence Related to Bernoulli Numbers
AU - Lin Jiu
AU - Yihang Yin
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05827
UR - https://arxiv.org/abs/2609.05827
AB - When exploring the Hankel determinant of the sequence μ_k=B_k+1/(k+1), where B_k is the k-th Bernoulli number, we obtained two interesting results. The first one applies in general to all sequences (c_k)_k≥0 with all even-indexed term $0$, except for c_0. In this case, the coefficient of the second highest order of the corresponding monic orthogonal polynomials determines the Hankel determinants. Our second result shows, the corresponding J-fractions, obtained from the generating function of μ_k, is exactly the same as in early work of Cao, on a faster sequence converging to the Euler--Mascheroni constant.
ER -