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

Author

Amiram Eldar, Aug 01 2025

Keywords

• nonn
• cons

Examples

			0.27606787380471479458379157265271548892384688537591...
		

Links

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

Crossrefs

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

Programs

Mathematica

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

PARI

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

Formula

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