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%I #39 May 27 2019 02:08:58
%S 8,0,8,8,9,4,9,3,0,1,2,7,2,1,1,3,8,9,0,5,2,9,0,1,6,5,6,5,9,0,3,5,3,5,
%T 4,5,6,2,4,3,4,3,0,4,9,8,0,4,5,1,0,0,4,6,9,4,7,5,5,0,6,1,7,7,7,2,2,9,
%U 7,1,9,6,1,1,8,1,6,3,3,3,0,3,9,2,6,0,6
%N Decimal expansion of AGHM(1,i,1+i)/(1+i), where i is the imaginary unit and AGHM stands for arithmetic-geometric-harmonic mean of a triple of numbers.
%C As AGM(x1,x2) is the well-known arithmetic-geometric mean of a pair of numbers x1 and x2, we can also define the AGHM(x1,x2,x3) as the arithmetic-geometric-harmonic mean of a triple of numbers x1, x2 and x3.
%C These three means were chosen because the arithmetic mean is the power mean with power = 1, the geometric mean is the power mean with power = 0 (lim_{power -> 0}) and the harmonic mean is the power mean with power = -1.
%C Definition of AGHM(x1,x2,x3), for arbitrary triple x1,x2,x3:
%C x1(0) = x1, x2(0) = x2, x3(0) = x3,
%C x1(n) = (x1(n-1) + x2(n-1) + x3(n-1))/3,
%C x2(n) = (x1(n-1) * x2(n-1) * x3(n-1))^(1/3),
%C x3(n) = 3/(1/x1(n-1) + 1/x2(n-1) + 1/x3(n-1)),
%C lim_{n -> inf} x1(n) = lim_{n -> inf} x2(n) = lim_{n -> inf} x3(n) = AGHM(x1,x2,x3).
%e 0.808894930127211...
%K nonn,cons
%O 0,1
%A _A.H.M. Smeets_, Sep 13 2018
%E More terms from _Jon E. Schoenfield_, May 26 2019
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