On the Series $sum^∞_{k=1} {3k}{k}^{-1}k^{-n}x^k$

[摘要] In this paper we investigate the series $sum^∞_{k=1}inom{3k}{k}^{-1}k^{-n}x^k$. Obtaining some integral representations of them, we evaluated the sum of them explicity for 𝑛=0,1,2.

[学科分类] 数学（综合）

[关键词] Inverse binomial series;hypergeometric series;polylogarithms;integral representations.