

A094090


Decimal expansion of positive solution to 5*(1exp(u)) + u*exp(u) = 0.


5



4, 9, 6, 5, 1, 1, 4, 2, 3, 1, 7, 4, 4, 2, 7, 6, 3, 0, 3, 6, 9, 8, 7, 5, 9, 1, 3, 1, 3, 2, 2, 8, 9, 3, 9, 4, 4, 0, 5, 5, 5, 8, 4, 9, 8, 6, 7, 9, 7, 2, 5, 0, 9, 7, 2, 8, 1, 4, 4, 4, 6, 1, 4, 4, 7, 8, 0, 4, 6, 3, 9, 8, 7, 9, 5, 7, 4, 5, 2, 9, 7, 2, 2, 3, 8, 2, 7, 0, 4, 5, 0, 6, 6, 0, 0, 0, 9, 6, 0, 8, 2, 9, 7, 7, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

This purely mathematical constant turns up when in physics one derives Wien's displacement law from the Planck blackbody radiation law (see link).
Positive solution to x = 5*(1exp(x)). More comments in A256500.  Stanislav Sykora, Apr 01 2015


LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..2000
NIST, Wien displacement law constant, in Fundamental Physical Constants.
Eric Weisstein's World of Physics, Wien's Displacement Law
Wikipedia, Planck's law


FORMULA

u = 5 + W(5*exp(5)), where W() is Lambert's Wfunction.


EXAMPLE

u=4.965114231744276...


MATHEMATICA

RealDigits[5 + ProductLog[ 5/E^5], 10, 120][[1]] (* Robert G. Wilson v, May 04 2004 *)


PROG

(PARI) a5=solve(x=0.1, 10, x5*(1exp(x))) \\ Use real precision in excess


CROSSREFS

Cf. A194567, A256500, A256501.
Sequence in context: A271181 A245299 A201415 * A200632 A186723 A008959
Adjacent sequences: A094087 A094088 A094089 * A094091 A094092 A094093


KEYWORD

cons,nonn


AUTHOR

Jeppe Stig Nielsen, May 01 2004


EXTENSIONS

More terms from Robert G. Wilson v, May 04 2004


STATUS

approved



