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%I #38 Feb 11 2013 13:52:00
%S 8,4,7,0,2,5,2,6,4,0,8,1,2,5,3,3,2,2,8,1,9,7,7,5,1,1,0,2,1,6,8,9,4,2,
%T 4,3,2,4,7,1,5,2,5,0,7,4,2,9,1,8,6,5,4,2,3,7,9,6,2,1,7,1,6,8,1,7,8,1,
%U 8,9,1,2,7,3,5,9,9,4,0,4,4,3,0,7,3,4,4,9,9,3,7,6,4,0,5,8,5,2,0,3,5,4,1,5,8,4
%N Decimal expansion of the argument z in (0,Pi/2) for which the function log(cos(sin(x)))/log(sin(cos(x))) possesses the maximum in (0,Pi/2).
%C We have max{f(x): x in (0,Pi/2)} = f(z) = A215832 = 0.641019237..., where f(x) = log(cos(sin(x)))/log(sin(cos(x))). See also A215833.
%D R. Witula, D. Jama, E. Hetmaniok, D. Slota, On some inequality of the trigonometric type, Zeszyty Naukowe Politechniki Slaskiej - Matematyka-Fizyka (Science Fascicle of Silesian Technical University - Math.-Phys.), 92 (2010), 83-92.
%e = 0.8470252640812533228197751102168942432471525...
%t f[x_] := Log[Cos[Sin[x]]] / Log[Sin[Cos[x]]]; x /. FindRoot[f'[x] == 0, {x, 1}, WorkingPrecision -> 130] // RealDigits[#, 10, 126]& // First (* _Jean-François Alcover_, Feb 11 2013 *)
%Y Cf. A215832, A215833, A215670, A215668, A216891.
%K nonn,cons
%O 0,1
%A _Roman Witula_, Aug 24 2012
%E Terms corrected by _Jean-François Alcover_, Feb 11 2013
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