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A275710 Decimal expansion of the Dirichlet eta function at 7.

%I A275710 #30 Aug 20 2021 04:25:19
%S A275710 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 A275710 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 A275710 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 A275710 Decimal expansion of the Dirichlet eta function at 7.
%F A275710 eta(7) = 63*zeta(7)/64 = (63*A013665)/64.
%F A275710 eta(7) = Lim_{n -> infinity} A334668(n)/A334669(n). - _Petros Hadjicostas_, May 07 2020
%F A275710 Equals Sum_{k>=1} (-1)^(k+1) / k^7. - _Sean A. Irvine_, Aug 19 2021
%e A275710 0.99259381992283028267...
%t A275710 RealDigits[63 Zeta[7]/64, 10, 100] [[1]]
%o A275710 (Sage) s = RLF(0); s
%o A275710 RealField(110)(s)
%o A275710 for i in range(1, 10000): s -= (-1)^i / i^7
%o A275710 print(s) # _Terry D. Grant_, Aug 06 2016
%o A275710 (PARI) -polylog(7, -1) \\ _Michel Marcus_, Aug 20 2021
%Y A275710 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 A275710 nonn,cons
%O A275710 0,1
%A A275710 _Terry D. Grant_, Aug 06 2016