A256593 Decimal expansion of 1/Pi*Integral_{0..Pi} x^2*log(2*cos(x/2))^2 dx, one of the log-cosine integrals related to zeta(4).

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

Offset

1,1

Links

Table of n, a(n) for n=1..102.

David Borwein and Jonathan M. Borwein, On an Intriguing Integral and Some Series Related to Zeta(4), Proc. Amer. Math. Soc. 123 (1995), 1191-1198

Formula

1/Pi*Integral_{0..Pi} x^2*log(2*cos(x/2))^2 dx = 11*Pi^4/180 = 11/2*zeta(4).

Example

5.952777785411260053338020330976423465261130235552997992256369...

Mathematica

RealDigits[11*Pi^4/180, 10, 102] // First

Crossrefs

Cf. A013662, A218505, A256568.

Sequence in context: A021172 A094880 A351216 * A275810 A302708 A108781

Adjacent sequences: A256590 A256591 A256592 * A256594 A256595 A256596

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 03 2015

Status

approved