|
|
A266389
|
|
Solution of the equation y(t) = 1, where function y(t) is defined in the Comments section.
|
|
12
|
|
|
6, 2, 6, 3, 7, 1, 6, 6, 3, 3, 0, 6, 4, 5, 1, 6, 6, 5, 8, 9, 2, 9, 9, 7, 8, 5, 0, 4, 5, 0, 3, 9, 5, 6, 1, 1, 6, 7, 2, 0, 8, 3, 1, 7, 8, 9, 3, 9, 8, 6, 0, 1, 4, 1, 1, 6, 1, 7, 8, 9, 8, 5, 4, 4, 9, 1, 7, 5, 2, 1, 5, 3, 0, 0, 2, 4, 2, 7, 7, 6, 7, 9, 0
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
For t in open interval (0,1) we have:
y1(t) = t^2 * (1-t) * (18 + 36*t + 5*t^2).
y2(t) = 2 * (3+t) * (1+2*t) * (1+3*t)^2.
y(t) = (1+2*t) / ((1+3*t)*(1-t)) * exp(-y1(t)/y2(t)) - 1.
|
|
LINKS
|
|
|
FORMULA
|
y(A266389) = 1, where function t->y(t) is defined in the Comments section.
|
|
EXAMPLE
|
0.62637166330...
|
|
PROG
|
(PARI)
y1(t) = t^2 * (1-t) * (18 + 36*t + 5*t^2);
y2(t) = 2 * (3+t) * (1+2*t) * (1+3*t)^2;
y(t) = (1+2*t) / ((1+3*t)*(1-t)) * exp(-y1(t)/y2(t)) - 1;
N=83; default(realprecision, N+100); t0 = solve(t=.62, .63, y(t)-1);
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|