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A267315 Decimal expansion of the Dirichlet eta function at 4.

%I A267315 #31 Feb 16 2025 08:33:29
%S A267315 9,4,7,0,3,2,8,2,9,4,9,7,2,4,5,9,1,7,5,7,6,5,0,3,2,3,4,4,7,3,5,2,1,9,
%T A267315 1,4,9,2,7,9,0,7,0,8,2,9,2,8,8,8,6,0,4,4,2,2,2,6,0,4,1,8,8,5,1,3,6,0,
%U A267315 5,5,3,9,1,6,3,5,9,7,7,4,0,7,3,7,2,9,5,9,3,1,4,4,8,9,8,7,4,2,7,5,7,8,8,6,6,9,6,2,1,6,9,5,3,7,3,9,9,6,1,2
%N A267315 Decimal expansion of the Dirichlet eta function at 4.
%H A267315 OEIS Wiki, <a href="https://oeis.org/wiki/Zeta_functions#Euler.27s_alternating_zeta_function">Euler's alternating zeta function</a>.
%H A267315 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>.
%H A267315 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet Eta Function</a>.
%F A267315 eta(4) = Sum_{k > 0} (-1)^(k+1)/k^4 = (7*Pi^4)/720.
%F A267315 eta(4) = Lim_{n -> infinity} A120296(n)/A334585(n) = (7/8)*A013662. - _Petros Hadjicostas_, May 07 2020
%e A267315 eta(4) = 1/1^4 - 1/2^4 + 1/3^4 - 1/4^4 + 1/5^4 - 1/6^4 + ... = 0.9470328294972459175765032344735219149279070829288860...
%t A267315 RealDigits[(7 Pi^4)/720, 10, 120][[1]]
%o A267315 (PARI) 7*Pi^4/720 \\ _Michel Marcus_, Feb 01 2016
%o A267315 (Magma) pi:= 7*Pi(RealField(110))^4 / 720; Reverse(Intseq(Floor(10^100*pi))); // _Vincenzo Librandi_, Feb 04 2016
%o A267315 (Sage) s = RLF(0); s
%o A267315 RealField(110)(s)
%o A267315 for i in range(1,10000): s += -((-1)^i/((i)^4))
%o A267315 print(s) # _Terry D. Grant_, Aug 04 2016
%Y A267315 Cf. A002162, A013662, A072691, A120296, A197070, A334585.
%K A267315 nonn,cons
%O A267315 0,1
%A A267315 _Ilya Gutkovskiy_, Jan 13 2016