A367899 Decimal expansion of limit_{n->oo} Product_{k=1..n} BarnesG(k/n)^(k/n^2).

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Eric Weisstein's World of Mathematics, Barnes G-Function.

Wikipedia, Barnes G-function.

Formula

Equals exp(1/24 + 3*zeta(3)/(8*Pi^2)) / (sqrt(A) * (2*Pi)^(1/12)), where A = A074962 is the Glaisher-Kinkelin constant.

Equals exp(Integral_{x=0..1} x*log(BarnesG(x)) dx).

Example

0.82679846439497137183536464944643006378339978236702912024106018188...

Mathematica

RealDigits[E^(1/24 + 3*Zeta[3]/(8*Pi^2))/(Sqrt[Glaisher]*(2*Pi)^(1/12)), 10, 120][[1]]
Exp[Integrate[x*Log[BarnesG[x]], {x, 0, 1}]]

Crossrefs

Cf. A074962, A367842, A367898.

Sequence in context: A019635 A011468 A120219 * A240976 A377400 A199158

Adjacent sequences: A367896 A367897 A367898 * A367900 A367901 A367902

Keyword

nonn,cons

Author

Vaclav Kotesovec, Dec 04 2023

Status

approved