“School of Mathematics”
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| Paper IPM / M / 11495 |
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| Abstract: | |||||
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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 [4/(π)], [(G)/(π)]
(where G is Catalan's constant), [(ζ′(2))/(π2)] and
also for logarithms of the Somos and Glaisher-Kinkelin constants.
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