|
|
A202539
|
|
Decimal expansion of the number x satisfying e^(2x)-e^(-x)=1.
|
|
2
|
|
|
2, 8, 1, 1, 9, 9, 5, 7, 4, 3, 2, 2, 9, 6, 1, 8, 4, 6, 5, 1, 2, 0, 5, 0, 7, 6, 4, 0, 6, 7, 8, 7, 8, 2, 9, 9, 7, 9, 2, 0, 2, 3, 2, 2, 5, 7, 4, 4, 0, 6, 6, 4, 6, 2, 6, 7, 5, 7, 3, 0, 3, 3, 4, 3, 1, 8, 0, 3, 8, 4, 5, 3, 0, 6, 2, 1, 2, 0, 8, 9, 1, 3, 2, 2, 9, 8, 7, 7, 0, 7, 4, 7, 5, 4, 9, 4, 0, 5, 4
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
See A202537 for a guide to related sequences. The Mathematica program includes a graph.
|
|
LINKS
|
|
|
FORMULA
|
Equals log((v^2+12)/(6*v)) with v = (108+12*sqrt(69))^(1/3). - Alois P. Heinz, Jul 14 2022
|
|
EXAMPLE
|
x=0.281199574322961846512050764067878299792023...
|
|
MATHEMATICA
|
u = 2; 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, .2, .3}, WorkingPrecision -> 110]
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|