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A347059 Decimal expansion of the Dirichlet eta function at 9.

%I A347059 #19 Aug 06 2024 05:54:29
%S A347059 9,9,8,0,9,4,2,9,7,5,4,1,6,0,5,3,3,0,7,6,7,7,8,3,0,3,1,8,5,2,5,9,7,9,
%T A347059 5,0,8,7,4,3,3,3,9,5,3,5,3,7,8,7,7,4,7,2,3,4,3,3,2,8,6,6,0,3,7,8,8,8,
%U A347059 7,4,5,5,5,2,5,4,5,2,7,0,2,0,7,9,4,9,3
%N A347059 Decimal expansion of the Dirichlet eta function at 9.
%D A347059 L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (306).
%H A347059 Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's catalog of the real numbers</a> (2011).
%F A347059 Equals (255/256) * zeta(9).
%F A347059 Equals Sum_{k>=1} (-1)^(k+1) / k^9.
%F A347059 Equals eta(9).
%e A347059 0.998094297541605330767783031852597950...
%t A347059 First[RealDigits[N[DirichletEta[9],87]]] (* _Stefano Spezia_, Aug 15 2021 *)
%o A347059 (PARI) -polylog(9, -1) \\ _Michel Marcus_, Aug 15 2021
%Y A347059 Cf. A072691, A197070, A267315, A267316, A275703, A275710, A347150, A346927.
%K A347059 nonn,cons
%O A347059 0,1
%A A347059 _Sean A. Irvine_, Aug 14 2021