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Using Known Zeta-Series to Derive the Dancs-He Series for $\,\ln{2}\,$ and $\,\zeta{(2\,n+1)}$ |
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PP: 121-124 |
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doi:10.18576/jant/040206
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Author(s) |
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Fabio M. S. Lima,
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Abstract |
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| In a recent work, Dancs and He found new formulas for ln2 and z (2n+1), n being a positive integer, which are expressed
in terms of Euler polynomials, each containing a series that apparently can not be evaluated in closed form, distinctly from z (2n),
for which the Euler’s formula allows us to write it as a rational multiple of p2n. There in that work, however, the formulas are
derived through certain series manipulations, by following Tsumura’s strategy, which makes it curious—in the words of those authors
themselves — the appearance of the number ln2. In this note, I show how some known zeta-series can be used to derive the Dancs-He
series in an alternative manner. |
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