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
Charles R Greathouse IV, Sep 01 2024
STATUS
approved