OFFSET
1,1
COMMENTS
Integral_{x=0..Pi/2, y=0..Pi/2} log(4*cos(x)^2 + 4*cos(y)^2) dy dx = G*Pi, where G is Catalan's constant A006752.
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..200
FORMULA
Equals limit_{n->infinity} Pi^3 * log(A340182(n)) / (8*n^3).
Equals Pi^3 * log(2)/8 + Integral_{x=0..Pi/2, y=0..Pi/2, z=0..Pi/2} log(3 + cos(2*x) + cos(2*y) + cos(2*z)) dz dy dx.
EXAMPLE
6.485696465218497693708581372103315764152266325617976316831738842452555238784...
MAPLE
evalf(Integrate(log(4*cos(x)^2 + 4*cos(y)^2 + 4*cos(z)^2), x = 0..Pi/2, y = 0..Pi/2, z = 0..Pi/2));
PROG
(PARI) intnum(x = 0, Pi/2, intnum(y = 0, Pi/2, intnum(z = 0, Pi/2, log(4*cos(x)^2 + 4*cos(y)^2 + 4*cos(z)^2)))) \\ 20 valid digits
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Vaclav Kotesovec, Jan 04 2021
STATUS
approved