%I #15 Mar 03 2022 05:14:38
%S 8,3,4,9,3,0,1,1,0,6,3,6,2,2,3,5,9,3,5,1,0,3,3,8,6,9,0,7,7,8,2,2,1,6,
%T 6,0,2,8,6,6,0,3,2,2,5,0,1,2,2,4,4,3,5,5,1,3,7,4,7,8,3,9,9,2,0,8,3,5,
%U 7,6,6,5,2,3,9,4,5,6,4,1,1,2,1,2,8,1,9,4,4,8,6,3,2,4,5,6,8,9,2,7,0,0,6
%N Decimal expansion of the triple integral Integral_{z = 0..1} Integral_{y = 0..1} Integral_{x = 0..1} (x*y*z)^(x*y*z) dx dy dz.
%C The double integral Integral_{y = 0..1} Integral_{x = 0..1} (x*y)^(x*y) dx dy equals Integral_{x = 0..1} x^x dx, which is listed as A083648.
%F The triple integral is most conveniently estimated from the identity Integral_{z = 0..1} Integral_{y = 0..1} Integral_{z = 0..1} (x*y*z)^(x*y*z) dx dy dz = (1/2)*Sum_{n >= 1} (-1)^(n+1)*(1/n^n + 1/n^(n+1)).
%e 0.83493011063622359351...
%t digits = 103; 1/2*NSum[ (-1)^(n+1)*(1/n^n + 1/n^(n+1)), {n, 1, Infinity}, WorkingPrecision -> digits+10, NSumTerms -> 100] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Feb 15 2013, from formula *)
%Y Cf. A073009, A083648, A209060.
%K nonn,easy,cons
%O 0,1
%A _Peter Bala_, Mar 04 2012