On the series $\pmb{\sum_{k = 1}^\infty \binom{3k}{k}^{-1}k^{-n} x^k}$

Details On the series $\pmb{\sum_{k = 1}^\infty \binom{3k}{k}^{-1}k^{-n} x^k}$ On the series $\pmb{\sum_{k = 1}^\infty \binom{3k}{k}^{-1}k^{-n} x^k}$

2005-12-14

arxiv.org/abs/math/0512310v1

Proc. Indian Acad. Sci. (Math. Sci.), Vol. 115, No. 4, November 2005, pp. 371-381

Mathematics

Commutative Algebra

11 pages

Scientific paper

In this paper we investigate the series $\sum_{k = 1}^\infty
\binom{3k}{k}^{-1}k^{-n}x^k$. Obtaining some integral representations of them,
we evaluated the sum of them explicitly for $n = 0, 1, 2$.

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