A340422 Decimal expansion of Integral_{x=0..Pi/2, y=0..Pi/2} log(1 + 2*sin(x)^2 + 2*sin(y)^2) dy dx.

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

Offset: 1

Author

Vaclav Kotesovec, Jan 07 2021

Keywords

• nonn
• cons

Examples

			2.551698806403924360993561678605629314325436926549295727591221339383517201757...
		

Crossrefs

Cf. A067518, A340322, A340350, A340421.

Programs

Mathematica

RealDigits[N[Pi*Integrate[(Log[1 + Sqrt[1 + 2/(3 - 2*Cos[x]^2)]] + Log[(1 + 2*Sin[x]^2)/4]/2), {x, 0, Pi/2}], 120], 10, 110][[1]]

Formula

Equals Pi * Integral_{x=0..Pi/2} (log(1 + sqrt(1 + 2/(3 - 2*cos(x)^2))) + log((1 + 2*sin(x)^2)/4)/2) dx.

Equals limit_{n->infinity} Pi^2 * log(A067518(n))/(4*n^2) - Pi^2*log(2)/4 - G*Pi, where G is Catalan's constant A006752.