Séminaire Lotharingien de Combinatoire, B53c (2005), 6 pp.

Wadim Zudilin

Computing Powers of Two Generalizations of the Logarithm

Abstract. 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).

Received: December 4, 2004. Accepted: May 22, 2005. Final Version: May 27, 2005.

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