A249649 Decimal expansion of Integral_{x = 0..1} Li_3(x) dx, where Li_3 is the trilogarithm function.
5, 5, 7, 1, 2, 2, 8, 3, 6, 3, 1, 1, 3, 6, 7, 8, 4, 8, 9, 2, 7, 3, 2, 2, 9, 9, 4, 8, 6, 5, 4, 2, 4, 8, 0, 1, 5, 4, 6, 0, 3, 6, 3, 9, 1, 1, 3, 3, 7, 0, 0, 4, 4, 4, 0, 5, 6, 7, 1, 3, 3, 2, 5, 9, 7, 1, 8, 3, 0, 7, 3, 5, 3, 8, 3, 1, 1, 2, 2, 1, 6, 3, 5, 2, 8, 2, 6, 9, 7, 2, 9, 8, 9, 5, 7, 6, 5, 5, 2, 8, 4, 2
Offset: 0
Examples
0.5571228363113678489273229948654248015460363911337...
Links
- Eric Weisstein's MathWorld, Trilogarithm
Programs
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Mathematica
RealDigits[1 - Zeta[2] + Zeta[3], 10, 102] // First
Formula
Integral_{x = 0..1} Li_3(x) dx = 1 - zeta(2) + zeta(3) = 1 - Pi^2/6 + zeta(3).
Compare with the same integral of the dilogarithm:
Integral_{x = 0..1} Li_2(x) dx = zeta(2) - 1 = Pi^2/6 - 1 = 0.644934...
Equals Sum_{n >= 1} 1/(n^4 + n^3). - Peter Bala, Aug 04 2025