A367899 - OEIS

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

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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...