A386737 Decimal expansion of Integral_{x=0..1} Integral_{y=0..1} Integral_{z=0..1} {1/(x+y+z)}^3 dx dy dz, where {} denotes fractional part.

2, 7, 6, 0, 6, 7, 8, 7, 3, 8, 0, 4, 7, 1, 4, 7, 9, 4, 5, 8, 3, 7, 9, 1, 5, 7, 2, 6, 5, 2, 7, 1, 5, 4, 8, 8, 9, 2, 3, 8, 4, 6, 8, 8, 5, 3, 7, 5, 9, 1, 3, 9, 5, 5, 5, 5, 0, 8, 4, 2, 0, 5, 1, 9, 0, 3, 4, 1, 4, 6, 1, 5, 0, 3, 4, 0, 7, 7, 6, 7, 4, 4, 0, 3, 3, 8, 9, 4, 8, 4, 5, 0, 9, 8, 6, 9, 0, 8, 5, 6, 3, 9, 9, 6, 6

Offset

0,1

Links

Table of n, a(n) for n=0..104.

Ovidiu Furdui, Multiple Fractional Part Integrals and Euler's Constant, Miskolc Mathematical Notes, Vol. 17, No. 1 (2016), pp. 255-266.

Formula

Equals log(3)/2 - 3*log(2)/2 + 5/3 - gamma/2 - zeta(2)/4 - zeta(3)/6.

Example

0.27606787380471479458379157265271548892384688537591...

Mathematica

RealDigits[Log[3]/2 - 3*Log[2]/2 + 5/3 - EulerGamma/2 - Zeta[2]/4 - Zeta[3]/6, 10, 120][[1]]

Prog

(PARI) log(3)/2 - 3*log(2)/2 + 5/3 - Euler/2 - zeta(2)/4 - zeta(3)/6

Crossrefs

Cf. A001620 (gamma), A002117, A002162, A002391, A013661, A386734, A386736.

Sequence in context: A193746 A070524 A259830 * A259235 A371801 A264692

Adjacent sequences: A386734 A386735 A386736 * A386738 A386739 A386740

Keyword

nonn,cons

Author

Amiram Eldar, Aug 01 2025

Status

approved