Vacca-Type Series for Values of the Generalized Euler Constant Function and its Derivative
Khodabakhsh Hessami Pilehrood and
Tatiana Hessami Pilehrood
Institute for Studies in Theoretical Physics and Mathematics
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.
Full version: pdf,
(Concerned with sequences
Received October 19 2009;
revised version received June 27 2010.
Published in Journal of Integer Sequences, July 9 2010.
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