A249649 - OEIS

A249649

Decimal expansion of integral_{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

int_{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:

int_{0..1} Li_2(x) dx = zeta(2) - 1 = Pi^2/6 - 1 = 0.644934...

EXAMPLE

0.5571228363113678489273229948654248015460363911337...