A247684 - OEIS

A247684

Decimal expansion of the integral over the first quadrant (x>0, y>0) of sqrt(x^2 + x*y + y^2)*exp(-x-y) dx dy.

%I #9 Sep 08 2022 08:46:09

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

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

%U 2,0,7,1,9,9,1,3,9,5,6,7,2,5,1,5,5,2,1,1,8,1,6,1,1,0,2,9,9,0,6,6,5,9

%N Decimal expansion of the integral over the first quadrant (x>0, y>0) of sqrt(x^2 + x*y + y^2)*exp(-x-y) dx dy.

%H G. C. Greubel, <a href="/A247684/b247684.txt">Table of n, a(n) for n = 1..10000</a>

%H 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 Equals 1 + (3/4)*log(3).

%e 1.8239592165010822685464339276918942784856179183670620888...

%t RealDigits[1 + (3/4)*Log[3], 10, 102] // First

%o (PARI) default(realprecision, 100); (4 + 3*log(3))/4 \\ _G. C. Greubel_, Sep 07 2018

%o (Magma) SetDefaultRealField(RealField(100)); (4 + 3*Log(3))/4; // _G. C. Greubel_, Sep 07 2018

%Y Cf. A244921, A247674, A247675, A247677.

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, Sep 22 2014