login
Decimal expansion of the number x satisfying x^2+3=e^x.
2

%I #8 Feb 07 2025 16:44:07

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

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

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

%N Decimal expansion of the number x satisfying x^2+3=e^x.

%C See A201741 for a guide to related sequences. The Mathematica program includes a graph.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.

%e x=1.87312254771304332172059709675425710408...

%t a = 1; b = 0; c = 3;

%t f[x_] := a*x^2 + b*x + c; g[x_] := E^x

%t Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]

%t r = x /. FindRoot[f[x] == g[x], {x, 1.8, 1.9}, WorkingPrecision -> 110]

%t RealDigits[r] (* A201742 *)

%Y Cf. A201741.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Dec 04 2011