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arXiv · 2609.05827

Partial Results on Hankel Determinants and the Corresponding J-Fractions of a Sequence Related to Bernoulli Numbers

Lin Jiu·Yihang Yin
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Abstract

When exploring the Hankel determinant of the sequence $\mu_{k}=B_{k+1}/(k+1)$, where $B_{k}$ is the $k$-th Bernoulli number, we obtained two interesting results. The first one applies in general to all sequences $(c_{k})_{k\geq0}$ 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 $\mu_{k}$, is exactly the same as in early work of Cao, on a faster sequence converging to the Euler--Mascheroni constant.

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Lin Jiu, Yihang Yin. 2026-09-05. Partial Results on Hankel Determinants and the Corresponding J-Fractions of a Sequence Related to Bernoulli Numbers. https://arxiv.org/abs/2609.05827

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