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Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet Eta Function</a>
Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet Eta Function</a>
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editing
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Continued fraction expansion of Sum_{k>=1} (-1)^(k - 1)/k^3 = (3*zeta(3))/4 = 0.901542677369695714...
allocated for Ilya GutkovskiyContinued fraction expansion of the Dirichlet eta function at 3.
0, 1, 9, 6, 2, 1, 1, 1, 1, 1, 1, 6, 1, 4, 1, 7, 2, 1, 1, 1, 2, 91, 32, 1, 1, 6, 23, 1, 1, 1, 1, 2, 9, 1, 2, 1, 1, 5, 1, 1, 37, 12, 1, 12, 3, 2, 87, 1, 4, 2, 2, 2, 320, 1, 7, 1, 2, 6, 3, 1, 6, 4, 1, 4, 2, 1, 69, 1, 4, 3, 3, 1, 14, 3, 1, 3, 1, 10, 2, 694, 2, 4, 21, 1, 1, 1, 3, 3, 10, 2, 1, 2, 2, 1, 3, 5, 1, 3, 9, 1
0,3
Continued fraction expansion of Sum_{k>=1} (-1)^(k - 1)/k^3 = (3*zeta(3))/4 = 0.901542677369695714...
OEIS Wiki, <a href="https://oeis.org/wiki/Zeta_functions#Euler.27s_alternating_zeta_function">Euler
Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet Eta Function</a>
Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>
<a href="/index/Con#confC">Index entries for continued fractions for constants</a>
1/1^3 - 1/2^3 + 1/3^3 - 1/4^3 + 1/5^3 - 1/6^3 +... = 1/(1 + 1/(9 + 1/(6 + 1/(2 + 1/(1 + 1/(1 + 1/...)))))).
ContinuedFraction[(3 Zeta[3])/4, 100]
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Ilya Gutkovskiy, Feb 26 2016
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