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We give continued fraction expansions of the generating functions ofBernoulli numbers, Cauchy numbers, Euler numbers, harmonic numbers, and theirgeneralized or related numbers. In particular, we focus on explicit forms ofthe convergents of these continued fraction expansions. Linear fractionaltransformations of such continued fractions are also discussed. We show morecontinued fraction expansion for different numbers and types, in particular, onCauchy numbers.

Continued fraction expansions of the generating functions of Bernoulli and related numbers