Vacca-Type Series for Values of the Generalized Euler Constant Function and its Derivative

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 log4/pi, G/pi (where G is Catalan's constant), zeta(2)/pi(2) and also for logarithms of Somos's and Glaisher-Kinkelin's constant