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%I #26 Nov 06 2022 09:11:59
%S 0,0,0,2,4,8,3,3,4,0,5,3,7,8,9,1,4,4,1,7,5,7,2,3,8,5,6,4,4,5,2,0,8,8,
%T 1,7,7,2,6,2,0,1,4,7,6,4,7,2,5,9,8,0,2,0,3,0,7,3,3,8,1,5,4,5,2,6,0,6,
%U 7,4,9,8,3,3,2,5,1,8,3,1,4,9,0,4,6,9,7,9,2,4,0,4,8,3,7,2,0,2,3,1,7,1,9,8,2,2,2,8,7,6,5,6,9,1,7,4,5,9
%N Decimal expansion of the constant B(2) = Sum_{n>=1} Sum_{m>=n+1} 1/(z(n)*z(m))^2 where z(n) is the imaginary part of the n-th nontrivial zero of the Riemann zeta function.
%F Equals (A332645^2 - A335815)/2.
%e 0.000248334053789144...
%t Join[{0, 0, 0}, RealDigits[N[-4*Catalan + Catalan^2/2 - Pi^2/2 + (Catalan*Pi^2)/8 + Pi^4/128 + (1/64)*Zeta[4, 1/4] + (2*Zeta'[1/2]^2)/Zeta[1/2]^2 - (Catalan Zeta'[1/2]^2)/(2 Zeta[1/2]^2) - (Pi^2 Zeta'[1/2]^2)/(16*Zeta[1/2]^2) - Zeta'[1/2]^4/(8*Zeta[1/2]^4) - (2 Zeta''[1/2])/Zeta[1/2] + (Catalan Zeta''[1/2])/(2 Zeta[1/2]) + (Pi^2 Zeta''[1/2])/(16*Zeta[1/2]) + Zeta'[1/2]^2*Zeta''[1/2]/(4 Zeta[1/2]^3) - Zeta'[1/2] Zeta'''[1/2]/(6 Zeta[1/2]^2) + Zeta''''[1/2]/(24 Zeta[1/2]), 115]][[1]]]
%Y Cf. A355283 (B(3)).
%Y Cf. A013629, A074760, A104539, A104540, A104541, A104542, A245275, A245276, A306339, A306340, A306341, A332645, A333360, A335814, A335815, A355283.
%K nonn,cons
%O 0,4
%A _Artur Jasinski_, Aug 23 2022
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