We generalize well-known Catalan-type integrals for Euler's constant to values of the generalized-Euler-constant function and its derivatives. Using generating functions appeared 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 Somos's and Glaisher-Kinkelin's constants.
Categories: math.NT