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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).
0
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
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
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved