A269443 - OEIS

%I #10 Feb 27 2016 10:36:57

%S 0,1,4,1,1,1,2,1,1,1,1,3,2,2,4,1,1,1,1,1,1,4,1,6,3,7,1,7,3,3,2,4,2,2,

%T 1,1,2,1,1,3,2,1,5,1,3,1,2,1,1,13,40,1,1,1,48,211,4,91,1,16,9,1,10,8,

%U 2,4,1,2,3,2,1,1,13,3,1,2,2,1,3,1,18,2,1,1,1,5,3,7,1,1,21,1,6,4,1,1,2,1,3,2

%N Continued fraction expansion of the Dirichlet eta function at 2.

%C Continued fraction expansion of Sum_{k>=1} (-1)^(k-1)/k^2 = Zeta(2)/2 = Pi^2/12 = 0.8224670334241132182362...

%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 1/1^2 - 1/2^2 + 1/3^2 - 1/4^2 + 1/5^2 - 1/6^2 +... = 1/(1 + 1/(4 + 1/(1 + 1/(1 + 1/(1 + 1/(2 + 1/...)))))).

%t ContinuedFraction[Pi^2/12, 100]

%o (PARI) contfrac(Pi^2/12) \\ _Michel Marcus_, Feb 26 2016

%Y Cf. A013679, A072691.

%K nonn,cofr

%O 0,3

%A _Ilya Gutkovskiy_, Feb 26 2016