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A245081 Decimal expansion of the position of the local maximum of the Barnes G function in the interval [0,2]. 3

%I

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

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

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

%N Decimal expansion of the position of the local maximum of the Barnes G function in the interval [0,2].

%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/BarnesG-Function.html">Barnes G-Function</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Barnes_G-function">Barnes G-function</a>

%F 3 - 2*x + log(2*Pi) + 2*(x-1)*psi(x-1) = 0, with 0<x<2, psi being the digamma function.

%e 1.39147038104109517345104885847432150030673503397700228177599677420531...

%t digits = 105; x1 = x /. FindRoot[3 - 2*x + Log[2*Pi] + 2*(x-1)*PolyGamma[x-1] == 0, {x, 3/2}, WorkingPrecision -> digits+10]; RealDigits[x1, 10, digits] // First

%Y Cf. A245082, A245083, A245084.

%K nonn,cons,easy

%O 1,2

%A _Jean-Fran├žois Alcover_, Jul 11 2014

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Last modified January 27 12:01 EST 2020. Contains 331295 sequences. (Running on oeis4.)