A247677 Decimal expansion of the integral over the square [0,Pi]x[0,Pi] of log(2-cos(x)-cos(y)) dx dy.

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

Offset: 1

Author

Jean-François Alcover, Sep 22 2014

Keywords

• nonn
• cons

Examples

			4.6692746625755280622628415121320951291596385520228...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• D. H. Bailey, J. M. Borwein, Highly Parallel, High-Precision Numerical Integration p. 9. (2005) Lawrence Berkeley National Laboratory

Crossrefs

Cf. A244921, A247674, A247675.

Programs

Magma

SetDefaultRealField(RealField(100)); R:= RealField(); 4*Pi(R)*Catalan(R) - Pi(R)^2*Log(2); // G. C. Greubel, Aug 31 2018

Mathematica

RealDigits[4*Pi*Catalan - Pi^2*Log[2], 10, 104] // First

PARI

4*Pi*Catalan - Pi^2*log(2) \\ Michel Marcus, Sep 22 2014

Formula

Equals 4*Pi*Catalan - Pi^2*log(2).