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

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, 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, 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

Offset

1,2

Links

Table of n, a(n) for n=1..105.

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 0<x<2, psi being the digamma function.

Example

1.39147038104109517345104885847432150030673503397700228177599677420531...

Mathematica

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

Crossrefs

Cf. A245082, A245083, A245084.

Sequence in context: A254348 A168399 A290375 * A010631 A355926 A019665

Adjacent sequences: A245078 A245079 A245080 * A245082 A245083 A245084

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 11 2014

Status

approved