A138285 - OEIS

%I #2 Mar 30 2012 17:22:47

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

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

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

%N Decimal expansion of the imaginary part of z0, the smallest second-quadrant solution of z = Cos(z).

%C z0 is a repelling fixed point of Cos(z). The only fixed point on the real axis is 0.73908... (A003957), which is an attracting fixed point.

%e 1.809361341295703319016276...

%t z0 = FindRoot[{Re[Cos[x+I*y]]==x, Im[Cos[x+I*y]]==y}, {{x,-2},{y,2}}, WorkingPrecision->150]; RealDigits[z0[[2,2]]]

%Y Cf. A138284 (real part).

%K cons,nonn

%O 1,2

%A _T. D. Noe_, Mar 12 2008