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

Author

Jean-François Alcover, Apr 03 2015

Keywords

• nonn
• cons
• easy

Examples

			5.952777785411260053338020330976423465261130235552997992256369...
		

Links

• 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

Crossrefs

Cf. A013662, A218505, A256568.

Programs

Mathematica

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

Formula

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