On the series ${\sum }_{k=1}^{\infty }{\left(\genfrac{}{}{0ex}{}{3k}{k}\right)}^{-1}{k}^{-n}{x}^k$

Abstract

In this paper we investigate the series ${\sum }_{k=1}^{\infty }{\left(\genfrac{}{}{0ex}{}{3k}{k}\right)}^{-1}{k}^{-n}{x}^k$. Obtaining some integral representations of them, we evaluated the sum of them explicitly for $n=0,1,2$.

11 pages