A202540 Decimal expansion of the number x satisfying e^(3x)-e^(-x)=1.

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

Offset: 0

Author

Clark Kimberling, Dec 21 2011

Keywords

• nonn
• cons

Comments

See A202537 for a guide to related sequences. The Mathematica program includes a graph.

Examples

			0.19946057824300535148857771838494917839277692...
		

Links

• Index entries for transcendental numbers

Crossrefs

Cf. A202537.

Programs

Mathematica

u = 3; v = 1;
f[x_] := E^(u*x) - E^(-v*x); g[x_] := 1
Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, .1, .2}, WorkingPrecision -> 110]
RealDigits[r]     (* A202540 *)
RealDigits[ Log[ Root[#^4 - # - 1&, 2]], 10, 99] // First (* Jean-François Alcover, Feb 27 2013 *)

PARI

log(polrootsreal(x^4-x-1)[2]) \\ Charles R Greathouse IV, May 14 2019