A375901 - OEIS

%I #9 Sep 04 2024 10:22:32

%S 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,

%T 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,

%U 3,5,6,9,5,5,5,3,6,6,7,1,2,5,7,5,1,7,5

%N Decimal expansion of the triple integral of {x/y}{y/z}{z/x} over the unit cube.

%H Cornel Ioan Vălean, <a href="https://ia601603.us.archive.org/20/items/1.pdf_almost/1.pdf.pdf">(Almost) Impossible Integrals, Sums, and Series</a>, Springer (2019), p. viii.

%F 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.

%F Vălean shows that this is equal to 1 - 3/4 * zeta(2) + 1/6 * zeta(2) * zeta(3).

%e 0.095850174913379525678536198596335370099479485204923539814301707481613569555....

%t RealDigits[1 + (Zeta[3]/6 - 3/4) * Zeta[2], 10, 120, -1][[1]] (* _Amiram Eldar_, Sep 03 2024 *)

%o (PARI) 1-.75*zeta(2)+zeta(2)*zeta(3)/6

%Y Cf. A002117, A013661, A183699.

%K nonn,cons

%O 0,2

%A _Charles R Greathouse IV_, Sep 01 2024