A256568 Decimal expansion of Integral_{0..Pi/2} x^2*log(cos(x))^2 dx, one of the log-cosine integrals related to zeta(3).

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

Offset

1,1

Links

Table of n, a(n) for n=1..105.

Mark W. Coffey, On some log-cosine integrals related to zeta(3), zeta(4), and zeta(6), Journal of Computational and Applied Mathematics 159 (2003) p. 207.

Formula

Pi/1440*(11*Pi^4 + 60*Pi^2*log(2)^2 + 720*log(2)*zeta(3)).

Example

4.26715236098409886523010918341815127892783395809205918285...

Mathematica

Pi/1440*(11*Pi^4 + 60*Pi^2*Log[2]^2 + 720*Log[2]*Zeta[3]) // RealDigits[#, 10, 105]& // First

Crossrefs

Cf. A002117.

Sequence in context: A135853 A338915 A173197 * A138947 A083412 A086399

Adjacent sequences: A256565 A256566 A256567 * A256569 A256570 A256571

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Apr 02 2015

Status

approved