A125578 Decimal expansion of positive root of x^2 = cos(x).

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

Offset: 0

Author

Denton J. Dailey (djd1497(AT)aol.com), Jan 03 2007

Keywords

• cons
• nonn

Comments

Both roots have same magnitude: x = +-0.824132312302...

Fixed point of cos(x)/x function. - Michal Paulovic, Jun 13 2023

Examples

			0.824132312302522422960956785771991108142689866748289991732...
		

Crossrefs

Cf. A003957, A124597.

Programs

Maple

Digits:=100;fsolve(cos(x)/x-x,x); # Michal Paulovic, Jun 13 2023

Mathematica

RealDigits[FindRoot[Cos[x] == x^2, {x, {.7, 1}}, WorkingPrecision -> 120][[1, 2, 1]], 10, 111][[1]]

PARI

solve(x=0,1,cos(x)-x^2) \\ Charles R Greathouse IV, Apr 14 2014