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Decimal expansion of the solution to x^2 = sin(x).
5

%I #8 Jun 13 2023 16:07:32

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

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

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

%N Decimal expansion of the solution to x^2 = sin(x).

%C Fixed point of cardinal sine (sinc) function. - _Michal Paulovic_, Jun 13 2023

%e 0.87672621539506244597211864314192813997168545140130499558964277342...

%p Digits:=105;fsolve(sin(x)/x-x,x); # _Michal Paulovic_, Jun 13 2023

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

%o (PARI) solve(x=0.8,0.9,sin(x)/x-x) \\ _Michal Paulovic_, Jun 13 2023

%Y Cf. A003957.

%K nonn,cons

%O 0,1

%A Denton J. Dailey (djd1497(AT)aol.com), Dec 18 2006

%E More terms from _Robert G. Wilson v_, Dec 21 2006