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Vacca-Type Series for Values of the Generalized Euler Constant Function and its Derivative
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Khodabakhsh Hessami Pilehrood and
Tatiana Hessami Pilehrood

Institute for Studies in Theoretical Physics and Mathematics

Tehran, Iran

**Abstract:**

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)/π^{2}, and also for logarithms of
the Somos and Glaisher-Kinkelin constants.

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(Concerned with sequences
A000120
A023416
A070939.)

Received October 19 2009;
revised version received June 27 2010.
Published in *Journal of Integer Sequences*, July 9 2010.

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