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A249649 Decimal expansion of integral_{0..1} Li_3(x) dx, where Li_3 is the trilogarithm function. 3
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 (list; constant; graph; refs; listen; history; text; internal format)
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...

MATHEMATICA

RealDigits[1 - Zeta[2] + Zeta[3], 10, 102] // First

CROSSREFS

Cf. A002117, A013661.

Sequence in context: A008705 A327242 A173932 * A226571 A274030 A061382

Adjacent sequences:  A249646 A249647 A249648 * A249650 A249651 A249652

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Nov 03 2014

STATUS

approved

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Last modified May 17 12:01 EDT 2021. Contains 343971 sequences. (Running on oeis4.)