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A269481 Continued fraction expansion of the Dirichlet eta function at 4.

%I A269481 #6 Feb 16 2025 08:33:30
%S A269481 0,1,17,1,7,3,3,1,7,3,6,1,1,7,1,11,1,11,5,1,2,2,2,7,1,14,6,5,1,1,1,1,
%T A269481 10,9,1,1,5,2,2,3,2,5,2,4,1,46,312,3,3,1,15,1,2,5,2,1,1,27,1,2,1,2,11,
%U A269481 5,2,1,482,3,2,4,2,2,3,1,3,1,2,1,1,13,1,13,1,1,67,149,7,2,2,18,1,2,1,1,1,51,1,7,1,8
%N A269481 Continued fraction expansion of the Dirichlet eta function at 4.
%C A269481 Continued fraction of Sum_{k>=1} (-1)^(k - 1)/k^4 = (7*Pi^4)/720 = 0.9470328294972459175765...
%H A269481 OEIS Wiki, <a href="https://oeis.org/wiki/Zeta_functions#Euler.27s_alternating_zeta_function">Euler's alternating zeta function</a>
%H A269481 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>
%H A269481 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet Eta Function</a>
%H A269481 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%e A269481 1/1^4 - 1/2^4 + 1/3^4 - 1/4^4 + 1/5^4 - 1/6^4 +... = 1/(1 + 1/(17 + 1/(1 + 1/(7 + 1/(3 + 1/(3 + 1/...)))))).
%t A269481 ContinuedFraction[(7 Pi^4)/720, 100]
%Y A269481 Cf. A013680, A267315.
%K A269481 nonn,cofr
%O A269481 0,3
%A A269481 _Ilya Gutkovskiy_, Feb 27 2016