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We generalize well-known Catalan-type integrals for Euler?fs constant to values of
the generalized Euler constant function and its derivatives. Using generating functions
appearing in these integral representations, we give new Vacca and Ramanujan-type
series for values of the generalized Euler constant function and Addison-type series for
values of the generalized Euler constant function and its derivative. As a consequence,
we get base-B rational series for log $\frac{4}{\pi}$, $\frac{G}{\pi}$
(where $G$ is Catalan's constant), $\frac{\zeta'(2)}{\pi^2}$ and
also for logarithms of the Somos and Glaisher-Kinkelin constants.
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