A249651 Decimal expansion of Integral_{0..1} Li_2(x)^2 dx, where Li_2 is the dilogarithm function.

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

Offset

0,1

Links

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

Pedro Freitas, Integrals of polylogarithmic functions, recurrence relations, and associated Euler sums, Math. Comput., Vol. 74, No. 251 (2005), pp. 1425-1440. See p. 1435, Table 3.

Eric Weisstein's World of Mathematics, Dilogarithm.

Formula

Equals 6 - 2*zeta(2) - 4*zeta(3) + zeta(2)^2.

Example

0.607712337943015464246226262015069415439032408...

Mathematica

RealDigits[6 - 2*Zeta[2] - 4*Zeta[3] + Zeta[2]^2, 10, 106] // First
(* Alternative: *)
NIntegrate[PolyLog[2, x]^2, {x, 0, 1}, WorkingPrecision->110] (* Vaclav Kotesovec, Nov 03 2014 *)

Prog

(Python)
from mpmath import *
mp.dps=107
f=lambda x: polylog(2, x)**2
I=quad(f, [0, 1])
print([int(n) for n in list(str(I)[2:-1])]) # Indranil Ghosh, Jul 04 2017
(PARI) (zeta(2)-1)^2 - 4*zeta(3) + 5 \\ Amiram Eldar, Jun 30 2026

Crossrefs

Cf. A002117, A013661, A249649, A397545, A397548, A397550, A397555.

Sequence in context: A195432 A196915 A374407 * A021626 A320376 A388110

Adjacent sequences: A249648 A249649 A249650 * A249652 A249653 A249654

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Nov 03 2014

Status

approved