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%I #13 Nov 05 2017 07:47:37
%S 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,
%T 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,
%U 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
%N Decimal expansion of the positive solution to x = 4*(1-exp(-x)).
%C 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.
%H Stanislav Sykora, <a href="/A256501/b256501.txt">Table of n, a(n) for n = 1..2000</a>
%H SpectralCalc, <a href="http://www.spectralcalc.com/blackbody/blackbody.html">Calculation of Blackbody Radiance</a>, Appendix C.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Planck%27s_law">Planck's law</a>
%e 3.9206903948728863435608913526135362205256273712079845304011750...
%t RealDigits[x/.FindRoot[x==4(1-Exp[-x]),{x,3},WorkingPrecision->120]] [[1]] (* _Harvey P. Dale_, May 08 2017 *)
%o (PARI) a4=solve(x=0.1, 10, x-4*(1-exp(-x))) \\ Use real precision in excess
%Y Cf. A094090 (q=5), A194567 (q=3), A256500 (q=2).
%K nonn,cons
%O 1,1
%A _Stanislav Sykora_, Apr 01 2015
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