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A346927 Decimal expansion of the Dirichlet eta function at 10.

%I A346927 #18 Aug 06 2024 05:55:11
%S A346927 9,9,9,0,3,9,5,0,7,5,9,8,2,7,1,5,6,5,6,3,9,2,2,1,8,4,5,6,9,9,3,4,1,8,
%T A346927 3,1,4,2,5,9,2,9,6,4,9,6,6,6,8,9,0,6,4,7,1,0,6,8,9,4,8,7,5,5,0,6,1,4,
%U A346927 2,4,5,8,3,8,4,0,3,8,1,2,4,4,0,7,9,8,5
%N A346927 Decimal expansion of the Dirichlet eta function at 10.
%D A346927 L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (306).
%H A346927 Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's catalog of the real numbers</a> (2011).
%H A346927 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A346927 Equals 73 * Pi^10 / (2^9 * 3^5 * 5 * 11).
%F A346927 Equals (511/512) * zeta(10).
%F A346927 Equals Sum_{k>=1} (-1)^(k+1) / k^10.
%F A346927 Equals eta(10).
%e A346927 0.999039507598271565639221845699341831425929649666890...
%t A346927 RealDigits[DirichletEta[10], 10, 100][[1]] (* _Amiram Eldar_, Aug 08 2021 *)
%o A346927 (PARI) -polylog(10, -1) \\ _Michel Marcus_, Aug 08 2021
%Y A346927 Cf. A072691, A197070, A267315, A267316, A275703, A275710, A347150, A347059.
%K A346927 nonn,cons
%O A346927 0,1
%A A346927 _Sean A. Irvine_, Aug 07 2021