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A269482 Continued fraction expansion of the Dirichlet eta function at 5.

%I A269482 #8 Feb 16 2025 08:33:30
%S A269482 0,1,34,1,6,1,1,3,1,2,1,1,1,2,1,2,1,1,2,2,2,35,3,1,5,4,1,2,2,1,4,1,1,
%T A269482 1,2,10,2,1,6,9,23,1,5,1,1,1,1,1,2,1,3,4,1,2,1,1,2,2,1,1,5,4,7,1,1,1,
%U A269482 1,2,2,1,4,1,1,2,8,3,2,1,3,1,5,356,2,57,6,1,6,1,1,31,1,5,1,1,477,1,9,7,3,4
%N A269482 Continued fraction expansion of the Dirichlet eta function at 5.
%C A269482 Continued fraction of Sum_{k>=1} (-1)^(k - 1)/k^5 = (15*zeta(5))/16 = 0.9721197704469093...
%H A269482 OEIS Wiki, <a href="https://oeis.org/wiki/Zeta_functions#Euler.27s_alternating_zeta_function">Euler's alternating zeta function</a>
%H A269482 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>
%H A269482 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet Eta Function</a>
%H A269482 <a href="/index/Con#confC">Index entries for continued fractions for constants</a>
%e A269482 1/1^5 - 1/2^5 + 1/3^5 - 1/4^5 + 1/5^5 - 1/6^5 +... = 1/(1 + 1/(34 + 1/(1 + 1/(6 + 1/(1 + 1/(1 + 1/...)))))).
%t A269482 ContinuedFraction[(15 Zeta[5])/16, 100]
%Y A269482 Cf. A013681, A267316.
%K A269482 nonn,cofr
%O A269482 0,3
%A A269482 _Ilya Gutkovskiy_, Feb 27 2016