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A267316 Decimal expansion of the Dirichlet eta function at 5.

%I A267316 #36 Jun 27 2025 23:40:06
%S A267316 9,7,2,1,1,9,7,7,0,4,4,6,9,0,9,3,0,5,9,3,5,6,5,5,1,4,3,5,5,3,4,6,9,5,
%T A267316 3,2,5,5,3,5,1,3,3,6,2,0,3,3,0,4,3,2,6,1,2,2,5,8,0,5,6,3,5,5,3,4,8,1,
%U A267316 5,8,6,5,4,2,4,6,3,8,8,9,1,7,7,5,0,4,0,4,1,2,3,9,7,3,1,2,5,0,2,8,5,5,8,9,4,0,7,0,1,2,4,8,9,6,8,2,0,9,7,7
%N A267316 Decimal expansion of the Dirichlet eta function at 5.
%H A267316 OEIS Wiki, <a href="https://oeis.org/wiki/Zeta_functions#Euler.27s_alternating_zeta_function">Euler's alternating zeta function</a>
%H A267316 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletEtaFunction.html">Dirichlet Eta Function</a>
%H A267316 Wikipedia, <a href="http://en.wikipedia.org/wiki/Dirichlet_eta_function">Dirichlet Eta Function</a>
%F A267316 Equals Sum_{k > 0} (-1)^(k+1)/k^5 = (15*zeta(5))/16.
%F A267316 Equals Lim_{n -> infinity} A136676(n)/A334604(n). - _Petros Hadjicostas_, May 07 2020
%e A267316 1/1^5 - 1/2^5 + 1/3^5 - 1/4^5 + 1/5^5 - 1/6^5 + ... = 0.972119770446909305935655143553469532553513362...
%t A267316 RealDigits[(15 Zeta[5])/16, 10, 120][[1]]
%o A267316 (PARI) 15*zeta(5)/16 \\ _Michel Marcus_, Feb 01 2016
%o A267316 (Sage) s = RLF(0); s
%o A267316 RealField(110)(s)
%o A267316 for i in range(1, 10000): s += -((-1)^i/((i)^5))
%o A267316 print(s) # _Terry D. Grant_, Aug 05 2016
%Y A267316 Cf. A002162 (value at 1), A013663, A072691 (value at 2), A197070 (value at 3), A267315 (value at 4), A136676, A334604.
%K A267316 nonn,cons
%O A267316 0,1
%A A267316 _Ilya Gutkovskiy_, Jan 13 2016