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

Proceedings Mathematical Sciences

Necdet Batir¹ 

[1] Department of Mathematics, Faculty of Arts and Sciences, Yüzüncü Yil University, 00 Van, Turkey$$

关键词: Inverse binomial series;    hypergeometric series;    polylogarithms;    integral representations.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 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.

【 授权许可】

Unknown