We give continued fraction expansions of the generating functions of Bernoulli numbers, Cauchy numbers, Euler numbers, harmonic numbers, and their generalized or related numbers. In particular, we focus on explicit forms of the convergents of these continued fraction expansions. Linear fractional transformations of such continued fractions are also discussed. We show more continued fraction expansion for different numbers and types, in particular, on Cauchy numbers.

中文翻译：

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伯努利和相关数的生成函数的连续分数展开式

我们给出了伯努利数、柯西数、欧拉数、调和数及其广义或相关数的生成函数的连分数展开式。特别地，我们关注这些连分数展开式收敛的显式形式。还讨论了这种连分数的线性分数变换。我们展示了不同数字和类型的更多连分数展开式，尤其是柯西数。