%I #16 Aug 20 2021 01:58:39
%S 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 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 2,4,5,8,3,8,4,0,3,8,1,2,4,4,0,7,9,8,5
%N Decimal expansion of the Dirichlet eta function at 10.
%D L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (306).
%H Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.366.9997">Shamos's catalog of the real numbers</a> (2011).
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals 73 * Pi^10 / (2^9 * 3^5 * 5 * 11).
%F Equals (511/512) * zeta(10).
%F Equals Sum_{k>=1} (-1)^(k+1) / k^10.
%F Equals eta(10).
%e 0.999039507598271565639221845699341831425929649666890...
%t RealDigits[DirichletEta[10], 10, 100][[1]] (* _Amiram Eldar_, Aug 08 2021 *)
%o (PARI) -polylog(10, -1) \\ _Michel Marcus_, Aug 08 2021
%Y Cf. A072691, A197070, A267315, A267316, A275703, A275710, A347150, A347059.
%K nonn,cons
%O 0,1
%A _Sean A. Irvine_, Aug 07 2021
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