cp's OEIS Frontend

A375506 Decimal expansion of the first derivative of the Dirichlet eta-function eta(s) at s=3/2.

%I A375506 #12 Aug 19 2024 03:14:05
%S A375506 1,2,8,6,7,4,7,5,0,8,3,0,3,5,7,1,9,0,0,9,5,9,5,2,9,2,9,9,1,0,3,0,1,3,
%T A375506 7,5,7,1,1,4,2,1,8,5,3,5,4,2,4,9,3,2,2,2,8,6,2,0,9,0,4,7,2,3,7,7,4,0,
%U A375506 7,0,1,6,5,6,0,8,8,8,7,6,8,2,8,1,1,8,9,4,1,3,2,0,9,2,6,3
%N A375506 Decimal expansion of the first derivative of the Dirichlet eta-function eta(s) at s=3/2.
%F A375506 Equals log(2)*zeta(3/2)/sqrt(2) +(1-1/sqrt(2))*zeta'(3/2)  = Sum_{i>=1} (-1)^i*log(i)/i^(3/2).
%e A375506 0.12867475083035719009595292991030137571142185354249...
%p A375506 s :=3/2 ; 2^(1-s)*log(2)*Zeta(s)+(1-2^(1-s))*Zeta(1,s) ; evalf(%) ;
%t A375506 RealDigits[DirichletEta'[3/2], 10, 120][[1]] (* _Amiram Eldar_, Aug 19 2024 *)
%Y A375506 Cf. A091812 (at s=1), A210593 (at s=2), A349220 (at s=3), A078434 (zeta(3/2)), A375503 (zeta'(3/2)).
%K A375506 nonn,cons
%O A375506 0,2
%A A375506 _R. J. Mathar_, Aug 18 2024