A367898 Decimal expansion of limit_{n->oo} Product_{k=1..n} BarnesG(k/n)^(1/n).

4, 1, 7, 4, 2, 7, 2, 9, 7, 6, 0, 1, 4, 0, 9, 8, 6, 3, 6, 4, 3, 9, 4, 8, 4, 5, 1, 6, 2, 2, 5, 1, 6, 9, 7, 7, 0, 9, 4, 5, 9, 6, 3, 3, 2, 2, 1, 4, 1, 1, 0, 0, 8, 2, 3, 2, 1, 1, 3, 1, 7, 6, 8, 2, 0, 0, 0, 9, 5, 8, 8, 8, 9, 2, 9, 8, 5, 6, 6, 3, 7, 9, 1, 9, 4, 6, 9, 5, 0, 3, 6, 9, 4, 0, 2, 4, 5, 7, 1, 4, 8, 2, 8, 0, 7, 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(1/12) / (A^2 * (2*Pi)^(1/4)), where A = A074962 is the Glaisher-Kinkelin constant.

Product_{k=1..n} BarnesG(k/n) = A^(1/n - n) * exp((n - 1/n)/12) * n^(1/2 + 1/(12*n)) * (2*Pi)^((1-n)/2) * Product_{k=1..n-1} Gamma(k/n)^(k/n).

Example

0.4174272976014098636439484516225169770945963322141100823211317682...

Mathematica

RealDigits[Exp[1/12] / (Glaisher^2 * (2*Pi)^(1/4)), 10, 120][[1]]

Crossrefs

Cf. A074962, A367842, A367899.

Sequence in context: A037022 A037023 A143971 * A016688 A143972 A019651

Adjacent sequences: A367895 A367896 A367897 * A367899 A367900 A367901

Keyword

nonn,cons

Author

Vaclav Kotesovec, Dec 04 2023

Status

approved