A138285 Decimal expansion of the imaginary part of z0, the smallest second-quadrant solution of z = Cos(z).

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, 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, 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

Offset: 1

Author

T. D. Noe, Mar 12 2008

Keywords

• cons
• nonn

Comments

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.

Examples

			1.809361341295703319016276...
		

Crossrefs

Cf. A138284 (real part).

Programs

Mathematica

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