English

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

Commutative Algebra 2007-05-23 v1

Abstract

In this paper we investigate the series k=1(3kk)1knxk\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=0,1,2n = 0, 1, 2.

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Cite

@article{arxiv.math/0512310,
  title  = {On the series $\pmb{\sum_{k = 1}^\infty \binom{3k}{k}^{-1}k^{-n} x^k}$},
  author = {Necdet Batir},
  journal= {arXiv preprint arXiv:math/0512310},
  year   = {2007}
}

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11 pages