Geodesic
Vacca-type series for values of the generalized Euler constant function and its derivative
Journal of integer sequences, Tome 13 (2010) no. 7
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 
@article{JIS_2010__13_7_a6,
     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},
     year = {2010},
     volume = {13},
     number = {7},
     zbl = {1203.11087},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2010__13_7_a6/}
}
TY  - JOUR
AU  - Hessami Pilehrood,  Khodabakhsh
AU  - Hessami Pilehrood,  Tatiana
TI  - Vacca-type series for values of the generalized Euler constant function and its derivative
JO  - Journal of integer sequences
PY  - 2010
VL  - 13
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/JIS_2010__13_7_a6/
LA  - en
ID  - JIS_2010__13_7_a6
ER  - 
%0 Journal Article
%A Hessami Pilehrood,  Khodabakhsh
%A Hessami Pilehrood,  Tatiana
%T Vacca-type series for values of the generalized Euler constant function and its derivative
%J Journal of integer sequences
%D 2010
%V 13
%N 7
%U http://geodesic.mathdoc.fr/item/JIS_2010__13_7_a6/
%G en
%F JIS_2010__13_7_a6
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/