A340350 Decimal expansion of Integral_{x=0..Pi/2, y=0..Pi/2} log(1 + sin(x)^2*sin(y)^2) dy dx.

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

Offset: 0

Author

Vaclav Kotesovec, Jan 05 2021

Keywords

• nonn
• cons

Examples

			0.49531661869212336430296504041161047588717884176797451824647459341123774...
		

Crossrefs

Cf. A097469, A340165, A340167, A340322, A340421, A340422.

Programs

Maple

evalf(Pi * Integrate(log((1 + sqrt(1 + sin(x)^2))/2), x = 0..Pi/2), 120);

Mathematica

RealDigits[N[Pi*Integrate[Log[(1 + Sqrt[1 + Sin[x]^2])/2], {x, 0, Pi/2}], 100]][[1]]

PARI

Pi * intnum(x = 0, Pi/2, log((1 + sqrt(1 + sin(x)^2))/2))

Formula

Equals Pi * Integral_{x=0..Pi/2} log((1 + sqrt(1 + sin(x)^2))/2) dx.

Equals limit_{n->infinity} Pi^2 * (log(A340165(n)) / (2*n^2) - log(2)).

Equals limit_{n->infinity} Pi^2 * (log(A340167(n)) / (4*n^2) - log(2)).