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

%I A247677 #11 Sep 08 2022 08:46:09
%S A247677 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,
%T A247677 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,
%U A247677 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
%N A247677 Decimal expansion of the integral over the square [0,Pi]x[0,Pi] of log(2-cos(x)-cos(y)) dx dy.
%H A247677 G. C. Greubel, <a href="/A247677/b247677.txt">Table of n, a(n) for n = 1..10000</a>
%H A247677 D. H. Bailey, J. M. Borwein, <a href="https://escholarship.org/uc/item/4281090t">Highly Parallel, High-Precision Numerical Integration</a> p. 9. (2005) Lawrence Berkeley National Laboratory
%F A247677 Equals 4*Pi*Catalan - Pi^2*log(2).
%e A247677 4.6692746625755280622628415121320951291596385520228...
%t A247677 RealDigits[4*Pi*Catalan - Pi^2*Log[2], 10, 104] // First
%o A247677 (PARI) 4*Pi*Catalan - Pi^2*log(2) \\ _Michel Marcus_, Sep 22 2014
%o A247677 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 4*Pi(R)*Catalan(R) - Pi(R)^2*Log(2); // _G. C. Greubel_, Aug 31 2018
%Y A247677 Cf. A244921, A247674, A247675.
%K A247677 nonn,cons
%O A247677 1,1
%A A247677 _Jean-François Alcover_, Sep 22 2014