A269444 - OEIS

%I #8 Mar 21 2016 11:46:53

%S 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,

%T 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,

%U 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

%N Continued fraction expansion of the Dirichlet eta function at 3.

%C Continued fraction expansion of Sum_{k>=1} (-1)^(k - 1)/k^3 = (3*zeta(3))/4 = 0.901542677369695714...

%H OEIS Wiki, <a href="https://oeis.org/wiki/Zeta_functions#Euler.27s_alternating_zeta_function">Euler's alternating zeta function</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet Eta Function</a>

%H <a href="/index/Con#confC">Index entries for continued fractions for constants</a>

%e 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/...)))))).

%t ContinuedFraction[(3 Zeta[3])/4, 100]

%Y Cf. A013631, A197070.

%K nonn,cofr

%O 0,3

%A _Ilya Gutkovskiy_, Feb 26 2016