login
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).
0

%I #7 Apr 03 2015 12:42:08

%S 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,

%T 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,

%U 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

%N 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).

%H David Borwein and Jonathan M. Borwein, <a href="http://dx.doi.org/10.1090/S0002-9939-1995-1231029-X">On an Intriguing Integral and Some Series Related to Zeta(4)</a>, Proc. Amer. Math. Soc. 123 (1995), 1191-1198

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

%e 5.952777785411260053338020330976423465261130235552997992256369...

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

%Y Cf. A013662, A218505, A256568.

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Apr 03 2015