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A375901
Decimal expansion of the triple integral of {x/y}{y/z}{z/x} over the unit cube.
0
0, 9, 5, 8, 5, 0, 1, 7, 4, 9, 1, 3, 3, 7, 9, 5, 2, 5, 6, 7, 8, 5, 3, 6, 1, 9, 8, 5, 9, 6, 3, 3, 5, 3, 7, 0, 0, 9, 9, 4, 7, 9, 4, 8, 5, 2, 0, 4, 9, 2, 3, 5, 3, 9, 8, 1, 4, 3, 0, 1, 7, 0, 7, 4, 8, 1, 6, 1, 3, 5, 6, 9, 5, 5, 5, 3, 6, 6, 7, 1, 2, 5, 7, 5, 1, 7, 5
OFFSET
0,2
LINKS
Cornel Ioan Vălean, (Almost) Impossible Integrals, Sums, and Series, Springer (2019), p. viii.
FORMULA
Integral_{0..1} Integral_{0..1} Integral_{0..1} {x/y}*{y/z}*{z/x} dx dy dz, where {w} is the fractional part of w.
Vălean shows that this is equal to 1 - 3/4 * zeta(2) + 1/6 * zeta(2) * zeta(3).
EXAMPLE
0.095850174913379525678536198596335370099479485204923539814301707481613569555....
MATHEMATICA
RealDigits[1 + (Zeta[3]/6 - 3/4) * Zeta[2], 10, 120, -1][[1]] (* Amiram Eldar, Sep 03 2024 *)
PROG
(PARI) 1-.75*zeta(2)+zeta(2)*zeta(3)/6
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
STATUS
approved