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A356693
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.
0
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, 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, 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
OFFSET
0,4
FORMULA
Equals (A332645^2 - A335815)/2.
EXAMPLE
0.000248334053789144...
MATHEMATICA
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]]]
KEYWORD
nonn,cons
AUTHOR
Artur Jasinski, Aug 23 2022
STATUS
approved