%I #14 Nov 21 2024 15:34:47

%S 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,

%T 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,

%U 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

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

%C This purely mathematical constant turns up when in physics one derives Wien's displacement law from the Planck black-body radiation law (see link).

%C Positive solution to x = 5*(1-exp(-x)). More comments in A256500. - _Stanislav Sykora_, Apr 01 2015

%H Stanislav Sykora, <a href="/A094090/b094090.txt">Table of n, a(n) for n = 1..2000</a>

%H NIST, <a href="http://physics.nist.gov/cgi-bin/cuu/Value?eqbwien">Wien displacement law constant</a>, in Fundamental Physical Constants.

%H Eric Weisstein's World of Physics, <a href="http://scienceworld.wolfram.com/physics/WiensDisplacementLaw.html">Wien's Displacement Law</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Planck%27s_law">Planck's law</a>

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F u = 5 + W(-5*exp(-5)), where W() is Lambert's W-function.

%e u=4.965114231744276...

%t RealDigits[5 + ProductLog[ -5/E^5], 10, 120][[1]] (* _Robert G. Wilson v_, May 04 2004 *)

%o (PARI) a5=solve(x=0.1, 10, x-5*(1-exp(-x))) \\ Use real precision in excess

%Y Cf. A194567, A256500, A256501.

%K cons,nonn

%O 1,1

%A _Jeppe Stig Nielsen_, May 01 2004

%E More terms from _Robert G. Wilson v_, May 04 2004