Geodesic
Computing Powers of Two Generalizations of the Logarithm
Séminaire lotharingien de combinatoire, Tome 53 (2005-2006) 
Wadim Zudilin. Computing Powers of Two Generalizations of the Logarithm. Séminaire lotharingien de combinatoire, Tome 53 (2005-2006). http://geodesic.mathdoc.fr/item/SLC_2005-2006_53_a2/
@article{SLC_2005-2006_53_a2,
     author = {Wadim Zudilin},
     title = {Computing {Powers} of {Two} {Generalizations} of the {Logarithm}},
     journal = {S\'eminaire lotharingien de combinatoire},
     year = {2005-2006},
     volume = {53},
     url = {http://geodesic.mathdoc.fr/item/SLC_2005-2006_53_a2/}
}
TY  - JOUR
AU  - Wadim Zudilin
TI  - Computing Powers of Two Generalizations of the Logarithm
JO  - Séminaire lotharingien de combinatoire
PY  - 2005-2006
VL  - 53
UR  - http://geodesic.mathdoc.fr/item/SLC_2005-2006_53_a2/
ID  - SLC_2005-2006_53_a2
ER  - 
%0 Journal Article
%A Wadim Zudilin
%T Computing Powers of Two Generalizations of the Logarithm
%J Séminaire lotharingien de combinatoire
%D 2005-2006
%V 53
%U http://geodesic.mathdoc.fr/item/SLC_2005-2006_53_a2/
%F SLC_2005-2006_53_a2

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

We prove multiple-series representations for positive integer powers of the series
\begin{displaymath} L(z;\alpha)=\sum_{n=1}^\infty\frac{z^n}{n+\alpha}, \;\; \ver... ...frac{z^nq^n}{1-q^n}, \;\; \vert z\vert\le1, \; \vert q\vert<1. \end{displaymath}

The results generalize a known formula for powers of the series for the ordinary logarithm -log(1-z) = L(z;0).