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%I #11 Mar 05 2013 05:12:30
%S 5,2,9,0,3,1,6,0,9,3,1,1,9,7,7,0,7,1,0,7,2,2,2,2,5,8,1,8,6,3,1,1,7,2,
%T 7,4,7,9,9,9,8,2,0,1,8,8,3,0,7,5,4,4,2,9,2,3,9,4,6,5,3,2,5,9,5,6,1,5,
%U 5,5,0,8,9,8,7,3,3,6,1,7,9,8,1,2,3,2,3,1,6,6,7,7,0,4,2,6,6,2,0,1,0,7,9,9,6
%N Decimal expansion of largest real root of e^x = Gamma(x+1).
%C This number corresponds to the point where the Gamma function starts to exceed the exponential function.
%H Robert Munafo, <a href="http://www.mrob.com/pub/math/numbers-2.html">Notable Properties of Specific Numbers</a>
%e x = 5.290316...
%t digits = 105; x /. FindRoot[E^x == Gamma[x+1], {x, 5}, WorkingPrecision -> digits+5] // RealDigits[#, 10, digits]& // First (* _Jean-François Alcover_, Mar 05 2013 *)
%o (PARI) solve(x=5.2,5.3,exp(x)-gamma(1+x))
%K cons,nonn
%O 1,1
%A _Robert G. Wilson v_, Nov 21 2002
%E More terms from _Benoit Cloitre_, Nov 25 2002
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