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A105168
Decimal expansion of a real root of x^Pi = e^x.
0
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, 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, 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
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Pi.
Eric Weisstein's World of Mathematics, e.
Eric Weisstein's World of Mathematics, Transcendental Equation.
FORMULA
Equals -Pi*LambertW(-1/Pi). - Vaclav Kotesovec, Apr 11 2021
EXAMPLE
1.73989894968180900...
MATHEMATICA
RealDigits[x/.FindRoot[x^Pi==E^x, {x, 1}, WorkingPrecision->130]][[1]] (* Harvey P. Dale, Jul 15 2012 *)
RealDigits[ -Pi*ProductLog[-1/Pi], 10, 103] // First (* Jean-François Alcover, Feb 27 2013 *)
PROG
(PARI) solve(x=1, 2, exp(x)-x^Pi) \\ Charles R Greathouse IV, Apr 15 2014
CROSSREFS
Sequence in context: A093525 A139340 A195725 * A134883 A201329 A084000
KEYWORD
cons,easy,nonn
AUTHOR
Jonathan Vos Post, Apr 10 2005
EXTENSIONS
Corrected and extended by Harvey P. Dale, Jul 15 2012
STATUS
approved