login
A294613
Decimal expansion of the ratio of the peak wavelength of Hawking radiation to the Schwarzchild radius of a black hole.
0
1, 5, 9, 0, 2, 3, 1, 9, 9, 7, 1, 5, 9, 4, 4, 5, 5, 9, 5, 4, 8, 2, 0, 6, 3, 9, 4, 5, 6, 1, 5, 7, 7, 4, 4, 7, 3, 7, 5, 5, 7, 9, 4, 2, 6, 0, 9, 0, 2, 2, 0, 8, 7, 4, 8, 0, 0, 1, 6, 0, 1, 8, 8, 9, 0, 3, 2, 2, 2, 7, 8, 4, 7, 6, 4, 7, 5, 2, 0, 4, 4, 5, 0, 0, 4, 8, 1, 6, 3, 4, 1, 6, 7, 8, 8, 4, 7, 7, 7, 7, 1, 1, 4, 3, 0
OFFSET
2,2
COMMENTS
The Hawking radiation has a black-body distribution with a wavelength given by Wien's displacement law.
REFERENCES
Mitchell Wick, Megaphysics III: Nothing Doesn’t Exist and Everything Does, AuthorHouse, 2017, Math Chapter 12.2.
FORMULA
Equals 8*Pi^2 / A094090.
EXAMPLE
15.9023199715944559548206394561577447375579426090220874800160188903222...
MATHEMATICA
RealDigits[8 Pi^2/(5 + ProductLog[-5/E^5]), 10, 111][[1]] (* Robert G. Wilson v, Nov 04 2017 *)
PROG
(PARI) 8*Pi^2/solve(x=0.1, 10, x-5*(1-exp(-x))) \\ Use real precision in excess
CROSSREFS
Cf. A094090.
Sequence in context: A175997 A249205 A344966 * A144408 A371323 A019636
KEYWORD
nonn,cons
AUTHOR
STATUS
approved