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

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, 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, 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

Offset

1,1

Links

Table of n, a(n) for n=1..106.

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

Cf. A245081, A245082, A245084.

Sequence in context: A021395 A004599 A197695 * A233565 A121359 A082087

Adjacent sequences: A245080 A245081 A245082 * A245084 A245085 A245086

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 11 2014

Status

approved