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Decimal expansion of the Dirichlet eta function at 7.
7

%I #30 Aug 20 2021 04:25:19

%S 9,9,2,5,9,3,8,1,9,9,2,2,8,3,0,2,8,2,6,7,0,4,2,5,7,1,3,1,3,3,3,9,3,6,

%T 8,5,2,3,1,1,1,5,6,9,2,4,3,1,4,0,6,8,5,1,6,2,9,5,1,3,0,8,7,5,6,2,6,7,

%U 0,2,0,5,2,1,8,6,4,7,0,5,1,9,8,1,3,1,4,2,0,3,7,7,4,5,7,2,3,9,7,0

%N Decimal expansion of the Dirichlet eta function at 7.

%F eta(7) = 63*zeta(7)/64 = (63*A013665)/64.

%F eta(7) = Lim_{n -> infinity} A334668(n)/A334669(n). - _Petros Hadjicostas_, May 07 2020

%F Equals Sum_{k>=1} (-1)^(k+1) / k^7. - _Sean A. Irvine_, Aug 19 2021

%e 0.99259381992283028267...

%t RealDigits[63 Zeta[7]/64, 10, 100] [[1]]

%o (Sage) s = RLF(0); s

%o RealField(110)(s)

%o for i in range(1, 10000): s -= (-1)^i / i^7

%o print(s) # _Terry D. Grant_, Aug 06 2016

%o (PARI) -polylog(7, -1) \\ _Michel Marcus_, Aug 20 2021

%Y Cf. A002162 (value at 1), A013665, A072691 (value at 2), A197070 (value at 3), A267315 (value at 4), A267316 (value at 5), A275703 (value at 6), A334668, A334669, A347150, A347059.

%K nonn,cons

%O 0,1

%A _Terry D. Grant_, Aug 06 2016