Chen, Hongwei Evaluations of some variant Euler sums. (English) Zbl 1101.11033 J. Integer Seq. 9, No. 2, Article 06.2.3, 9 p. (2006). This paper obtains closed form evaluations of various sums of the form \(\sum^\infty_{k=1} a_k h_k\), where \[ h_k= \sum^k_{r=1}(2^r- 1)^{-1} \] and \(a_k\) is a simple function of \(k\). Many of them are consequences of the power series expansion \[ \sum^\infty_{k=1} {h_k\over k} x^{2k}= {1\over 4}\log^2\Biggl({1+x\over 1-z}\Biggr). \] Reviewer: Tom M. Apostol (Pasadena) Cited in 2 ReviewsCited in 5 Documents MSC: 11M41 Other Dirichlet series and zeta functions 11M06 \(\zeta (s)\) and \(L(s, \chi)\) 40A05 Convergence and divergence of series and sequences Software:OEIS PDFBibTeX XMLCite \textit{H. Chen}, J. Integer Seq. 9, No. 2, Article 06.2.3, 9 p. (2006; Zbl 1101.11033) Full Text: EuDML EMIS