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Decimal expansion of (4/9)^(4/9) = (8/27)^(8/27).
3

%I #6 Mar 30 2012 19:00:09

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

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

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

%N Decimal expansion of (4/9)^(4/9) = (8/27)^(8/27).

%C (4/9)^(4/9) = (8/27)^(8/27) corresponds to (9/4)^(27/8) = (27/8)^(9/4) (see A194556) under the equivalence x^x = y^y <==> (1/x)^(1/y) = (1/y)^(1/x).

%H J. Sondow and D. Marques, <a href="http://arxiv.org/abs/1108.6096">Algebraic and transcendental solutions of some exponential equations</a>, Annales Mathematicae et Informaticae 37 (2010) 151-164; see p. 8 in the link.

%e 0.6973879457621430704075323673549042345770355186105029836376253048204852032246954...

%t RealDigits[(4/9)^(4/9), 10, 100] // First

%Y Cf. A194556.

%K nonn,cons

%O 0,1

%A _Jonathan Sondow_, Sep 02 2011