New relations among Euler sums of even weight

Authors

  • Wen-Chin Liaw

DOI:

https://doi.org/10.5556/j.tkjm.38.2007.91

Abstract

IIn this paper, we shall consider different kinds of Euler sums which are related to Ramanujan's constant $G(1)$. We develop new relations among these Euler sums and classical Euler sums of even weight. In particular, from these relations we give explicit evaluations of $$ G_{1, 2n+1} = \sum_{k=0}^{\infty} \frac{1}{(2k+1)^{2n+1}} \sum_{j=1}^{k} \frac{1}{j}. $$

Author Biography

Wen-Chin Liaw

Department of Mathematics, National Chung Cheng University, Minhsiung, Chiayi 62145, Taiwan

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Published

2007-03-31

How to Cite

Liaw, W.-C. (2007). New relations among Euler sums of even weight. Tamkang Journal of Mathematics, 38(1), 21-36. https://doi.org/10.5556/j.tkjm.38.2007.91

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Papers