Geodesic
Vacca-type series for values of the generalized Euler constant function and its derivative
Journal of integer sequences, Tome 13 (2010) no. 7.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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/\pi , G/\pi $ (where $G$ is Catalan's constant), $\zeta '(2)/\pi ^{2}$, and also for logarithms of the Somos and Glaisher-Kinkelin constants.
Classification : 11Y60, 65B10, 40A05, 05A15
Keywords: Euler constant, series summation, generating function, lerch transcendent, generalized somos constants, glaisher-kinkelin constant 
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     author = {Hessami Pilehrood, Khodabakhsh and Hessami Pilehrood, Tatiana},
     title = {Vacca-type series for values of the generalized {Euler} constant function and its derivative},
     journal = {Journal of integer sequences},
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Hessami Pilehrood, Khodabakhsh; Hessami Pilehrood, Tatiana. Vacca-type series for values of the generalized Euler constant function and its derivative. Journal of integer sequences, Tome 13 (2010) no. 7. http://geodesic.mathdoc.fr/item/JIS_2010__13_7_a6/