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Decimal expansion of the Dirichlet eta function at 9.
3

%I #19 Aug 06 2024 05:54:29

%S 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 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 7,4,5,5,5,2,5,4,5,2,7,0,2,0,7,9,4,9,3

%N Decimal expansion of the Dirichlet eta function at 9.

%D L. B. W. Jolley, Summation of Series, Dover, 1961, Eq. (306).

%H Michael I. Shamos, <a href="https://citeseerx.ist.psu.edu/pdf/ae33a269baba5e8b1038e719fb3209e8a00abec5">Shamos's catalog of the real numbers</a> (2011).

%F Equals (255/256) * zeta(9).

%F Equals Sum_{k>=1} (-1)^(k+1) / k^9.

%F Equals eta(9).

%e 0.998094297541605330767783031852597950...

%t First[RealDigits[N[DirichletEta[9],87]]] (* _Stefano Spezia_, Aug 15 2021 *)

%o (PARI) -polylog(9, -1) \\ _Michel Marcus_, Aug 15 2021

%Y Cf. A072691, A197070, A267315, A267316, A275703, A275710, A347150, A346927.

%K nonn,cons

%O 0,1

%A _Sean A. Irvine_, Aug 14 2021