A126585 - OEIS

%I #10 Nov 21 2024 15:41:27

%S 8,1,5,5,5,3,4,1,8,8,0,8,9,6,0,6,5,7,7,7,2,7,2,7,3,2,5,3,0,8,5,5,9,4,

%T 8,0,5,9,7,4,0,9,9,0,8,8,4,0,6,3,8,5,3,9,8,9,3,6,2,5,0,4,0,3,2,7,2,7,

%U 7,4,5,6,2,6,8,3,7,6,2,1,0,4,7,2,6,5,8,2,8,5,2,4,3,1,8,2,4,3,5,2,4,4

%N Decimal expansion of solution to exp(-x) = x^4.

%H G. C. Greubel, <a href="/A126585/b126585.txt">Table of n, a(n) for n = 0..10000</a>

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

%F Equals 4*LambertW(1/4). - _G. C. Greubel_, Mar 06 2018

%e 0.81555341880896065777272732530855948059740990884063853...

%t RealDigits[ FindRoot[ Exp[ -x] == x^4, {x, {.5, 1}}, WorkingPrecision -> 120][[1, 2, 1]], 10, 111][[1]]

%t RealDigits[ 4*ProductLog[1/4], 10, 102] // First (* _Jean-François Alcover_, Feb 27 2013 *)

%o (PARI) 4*lambertw(1/4) \\ _G. C. Greubel_, Mar 06 2018

%Y Cf. A030178.

%K cons,nonn

%O 0,1

%A Denton J. Dailey (denton.dailey(AT)bc3.edu), Jan 05 2007