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Paper IPM / M / 11495  


Abstract:  
We generalize wellknown Catalantype 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 Ramanujantype
series for values of the generalized Euler constant function and Addisontype series for
values of the generalized Euler constant function and its derivative. As a consequence,
we get baseB rational series for log [4/(π)], [(G)/(π)]
(where G is Catalan's constant), [(ζ′(2))/(π^{2})] and
also for logarithms of the Somos and GlaisherKinkelin constants.
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