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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

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..101.

Eric Weisstein's MathWorld, Trilogarithm

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

EXAMPLE