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A259928
Decimal expansion of the infinite double sum S = Sum_{m>=1} (Sum_{n>=1} 1/(m^2*n*(m+n)^3)).
0
1, 6, 9, 5, 5, 7, 1, 7, 6, 9, 9, 7, 4, 0, 8, 1, 8, 9, 9, 5, 2, 4, 1, 9, 6, 5, 4, 9, 6, 5, 1, 5, 3, 4, 2, 1, 3, 1, 6, 9, 6, 9, 5, 8, 1, 6, 7, 2, 1, 4, 2, 2, 6, 0, 3, 0, 7, 0, 6, 8, 1, 1, 0, 6, 6, 7, 3, 8, 8, 6, 9, 7, 1, 5, 0, 3, 2, 6, 3, 1, 6, 3, 1, 3, 7, 9, 5, 6, 6, 2, 9, 8, 9, 7, 5, 5, 8, 6, 1, 7, 5, 5, 0
OFFSET
0,2
FORMULA
S = (7/4)*zeta(6) - zeta(3)^2/2 - sum_{m>=1} (PolyGamma(1, m+1)/m^4) + (1/2)*sum_{m>=1} (PolyGamma(2, m+1)/m^3), where sum_{m>=1} (PolyGamma(1, m+1)/m^4) is A258989, the second sum being A259927.
S simplifies to zeta(6)/6 = Pi^6/5670.
2*A258987 + 6*S = zeta(3)^2.
EXAMPLE
0.16955717699740818995241965496515342131696958167214226030706811...
MATHEMATICA
RealDigits[Pi^6/5670, 10, 103] // First
PROG
(PARI) Pi^6/5670 \\ Michel Marcus, Jul 09 2015
CROSSREFS
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved