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A245083 Decimal expansion of the position of the local minimum of the Barnes G function in the interval [2,4]. 3

%I

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

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

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

%N Decimal expansion of the position of the local minimum of the Barnes G function in the interval [2,4].

%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 2<x<4, psi being the digamma function.

%e 2.557663932789019434221440600499355020352290831999042648242562174186...

%t digits = 105; x2 = x /. FindRoot[3 - 2*x + Log[2*Pi] + 2*(x-1)*PolyGamma[x-1] == 0, {x, 3}, WorkingPrecision -> digits+10]; RealDigits[x2, 10, digits] // First

%Y Cf. A245081, A245082, A245084.

%K nonn,cons,easy

%O 1,1

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

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Last modified December 6 19:31 EST 2019. Contains 329809 sequences. (Running on oeis4.)