|
|
A256501
|
|
Decimal expansion of the positive solution to x = 4*(1-exp(-x)).
|
|
4
|
|
|
3, 9, 2, 0, 6, 9, 0, 3, 9, 4, 8, 7, 2, 8, 8, 6, 3, 4, 3, 5, 6, 0, 8, 9, 1, 3, 5, 2, 6, 1, 3, 5, 3, 6, 2, 2, 0, 5, 2, 5, 6, 2, 7, 3, 7, 1, 2, 0, 7, 9, 8, 4, 5, 3, 0, 4, 0, 1, 1, 7, 5, 0, 0, 5, 7, 9, 0, 5, 0, 5, 6, 4, 8, 3, 6, 6, 7, 0, 5, 7, 5, 7, 4, 3, 3, 6, 5, 6, 6, 0, 1, 8, 9, 4, 8, 3, 6, 5, 8, 9, 0, 4, 7, 3, 0
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Each of the positive solutions to x = q*(1-exp(-x)) obtained for q = 2, 3, 4, and 5, appears in several formulas pertinent to Planck's black-body radiation law. For a given q, the solution can be also written as q+W(-q/exp(q)), where W is the Lambert function. Here q = 4.
|
|
LINKS
|
|
|
EXAMPLE
|
3.9206903948728863435608913526135362205256273712079845304011750...
|
|
MATHEMATICA
|
RealDigits[x/.FindRoot[x==4(1-Exp[-x]), {x, 3}, WorkingPrecision->120]] [[1]] (* Harvey P. Dale, May 08 2017 *)
|
|
PROG
|
(PARI) a4=solve(x=0.1, 10, x-4*(1-exp(-x))) \\ Use real precision in excess
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|