A397548 Decimal expansion of Integral_{0..1} Li_2(x)^4 dx, where Li_2 is the dilogarithm function.

8, 1, 8, 0, 5, 2, 8, 7, 4, 0, 4, 1, 7, 0, 9, 0, 2, 9, 7, 2, 8, 8, 0, 8, 8, 7, 9, 9, 1, 9, 8, 7, 7, 7, 0, 1, 7, 3, 8, 6, 2, 6, 0, 2, 1, 6, 8, 6, 6, 8, 1, 2, 4, 2, 2, 8, 3, 0, 4, 6, 8, 4, 3, 5, 9, 8, 5, 5, 6, 0, 9, 7, 6, 7, 5, 2, 2, 8, 3, 0, 6, 1, 9, 3, 5, 2, 9, 7, 2, 3, 0, 9, 4, 3, 3, 3, 2, 9, 3, 1, 1, 0, 8, 2, 7, 8

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Eric Weisstein's World of Mathematics, Dilogarithm.

Formula

Equals 2520 - 60*Pi^2 - 43*Pi^4/5 - 11*Pi^6/1890 + Pi^8/1296 - 720*zeta(3) + 24*Pi^2*zeta(3) + 14*Pi^4*zeta(3)/15 + 144*zeta(3)^2 - 648*zeta(5) + 4*Pi^2*zeta(5) - 195*zeta(7).

Example

0.8180528740417090297288088799198777017386260216866812422830468435...

Mathematica

RealDigits[2520 - 60*Pi^2 - 43*Pi^4/5 - 11*Pi^6/1890 + Pi^8/1296 - 720*Zeta[3] + 24*Pi^2*Zeta[3] + 14*Pi^4*Zeta[3]/15 + 144*Zeta[3]^2 - 648*Zeta[5] + 4*Pi^2*Zeta[5] - 195*Zeta[7], 10, 110][[1]]
(* Alternative: *)
NIntegrate[PolyLog[2, x]^4, {x, 0, 1}, WorkingPrecision->110]

Crossrefs

Cf. A249651, A397545.

Sequence in context: A143548 A231929 A154460 * A021554 A021059 A010689

Adjacent sequences: A397544 A397545 A397547 * A397549 A397550 A397551

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jun 30 2026

Status

approved