OFFSET
1,1
LINKS
Eric Weisstein's MathWorld, Barnes G-Function
Wikipedia, Barnes G-function
FORMULA
3 - 2*x + log(2*Pi) + 2*(x-1)*psi(x-1) = 0, with 2<x<4, psi being the digamma function.
EXAMPLE
2.557663932789019434221440600499355020352290831999042648242562174186...
MATHEMATICA
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
CROSSREFS
KEYWORD
AUTHOR
Jean-François Alcover, Jul 11 2014
STATUS
approved