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