%I #24 Feb 16 2025 08:32:57
%S 1,7,3,9,8,9,8,9,4,9,6,8,1,8,0,9,0,0,4,9,1,1,4,7,5,8,6,9,9,7,8,1,1,1,
%T 5,1,9,3,2,9,6,8,0,0,9,3,5,6,2,4,7,5,7,4,6,9,5,8,8,1,7,1,4,7,5,6,3,6,
%U 2,7,0,2,0,6,5,4,3,7,3,0,0,1,8,2,7,4,5,4,3,4,1,8,9,5,0,8,6,9,2,2,9,9,9
%N Decimal expansion of a real root of x^Pi = e^x.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Pi.html">Pi</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/e.html">e</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TranscendentalEquation.html">Transcendental Equation</a>.
%F Equals -Pi*LambertW(-1/Pi). - _Vaclav Kotesovec_, Apr 11 2021
%e 1.73989894968180900...
%t RealDigits[x/.FindRoot[x^Pi==E^x,{x,1},WorkingPrecision->130]][[1]] (* _Harvey P. Dale_, Jul 15 2012 *)
%t RealDigits[ -Pi*ProductLog[-1/Pi], 10, 103] // First (* _Jean-François Alcover_, Feb 27 2013 *)
%o (PARI) solve(x=1,2,exp(x)-x^Pi) \\ _Charles R Greathouse IV_, Apr 15 2014
%Y Cf. A000796, A001113.
%K cons,easy,nonn,changed
%O 1,2
%A _Jonathan Vos Post_, Apr 10 2005
%E Corrected and extended by _Harvey P. Dale_, Jul 15 2012