|
|
A199736
|
|
Decimal expansion of greatest x satisfying x^2-4*x*cos(x)=2*sin(x).
|
|
3
|
|
|
1, 5, 1, 9, 5, 1, 4, 9, 2, 6, 4, 7, 0, 4, 0, 1, 2, 2, 1, 5, 8, 5, 7, 0, 5, 1, 6, 2, 0, 9, 8, 1, 4, 8, 9, 9, 0, 5, 5, 6, 3, 3, 9, 8, 8, 6, 8, 9, 3, 4, 3, 5, 6, 3, 8, 8, 5, 1, 9, 2, 1, 5, 1, 6, 1, 7, 9, 8, 1, 3, 3, 8, 5, 2, 1, 7, 2, 7, 8, 9, 7, 2, 6, 8, 0, 2, 0, 5, 3, 1, 2, 0, 1, 8, 1, 2, 1, 6, 3
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
See A199597 for a guide to related sequences. The Mathematica program includes a graph.
|
|
LINKS
|
|
|
EXAMPLE
|
least: -3.69221424543584046112101682937268753850...
greatest: 1.519514926470401221585705162098148990...
|
|
MATHEMATICA
|
a = 1; b = -4; c = 2;
f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c*Sin[x]
Plot[{f[x], g[x]}, {x, -4, 2}, {AxesOrigin -> {0, 0}}]
r = x /. FindRoot[f[x] == g[x], {x, -3.7, -3.6}, WorkingPrecision -> 110]
RealDigits[r] (* A199735 least root *)
r = x /. FindRoot[f[x] == g[x], {x, 1.5, 1.6}, WorkingPrecision -> 110]
RealDigits[r] (* A199736 greatest root *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|