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A258500 Decimal expansion of the nontrivial real solution of x^(3/2) = (3/2)^x. 2

%I #11 Dec 10 2016 19:37:41

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

%T 3,8,9,8,0,4,1,7,1,1,4,1,0,7,4,0,0,0,1,5,1,8,2,2,7,1,8,3,9,3,7,9,1,7,

%U 0,7,1,7,1,0,0,1,3,8,4,0,2,2,8,4,2,1,8,2,3,1,1,9,2,3,0,4,7,0,6,6,7

%N Decimal expansion of the nontrivial real solution of x^(3/2) = (3/2)^x.

%H Jonathan Sondow, Diego Marques, <a href="http://arxiv.org/abs/1108.6096">Algebraic and transcendental solutions of some exponential equations</a>, Annales Mathematicae et Informaticae 37 (2010) 151-164.

%F x0 = -((x*ProductLog(-1, -(log(x)/x)))/log(x)), with x = 3/2, where ProductLog is the Lambert W function.

%e x0 = 7.408764686965774521957295028510614389804171141074...

%e z = x0^(3/2) = 20.16595073003535058942970947434890012034363496 ...

%e z > e^e = 15.15426224... = A073226.

%t x0 = -((x*ProductLog[-1, -(Log[x]/x)])/Log[x]) /. x -> 3/2; RealDigits[x0, 10, 101] // First

%Y Cf. A073226, A194556, A194557, A258501 (x^(5/2)=(5/2)^x), A258502 (x^(7/2)=(7/2)^x).

%K nonn,cons,easy

%O 1,1

%A _Jean-François Alcover_, Jun 01 2015

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)