The Barnes G-function is an analytic continuation of the G-function defined in the construction of the Glaisher-Kinkelin constant G(n) congruent [Γ(n)]^(n - 1)/(H(n - 1)) for n>0, where H(n) is the hyperfactorial, which has the special values G(n) = {0 | if n = 0, -1, -2, ... 1 | if n = 1 0!1!2!...(n - 2)! | if n = 2, 3, ... auto right match for integer n. This function is a shifted version of the superfactorial with values for n = 0, 1, 2, ... given by 0, 1, 1, 1, 2, 12, 288, 34560, 24883200, 125411328000, 5056584744960000, ... (OEIS A000178).

Euler-Mascheroni constant | G-function | Glaisher-Kinkelin constant | hyperfactorial | K-function | Meijer G-function | Ramanujan g- and G-functions | superfactorial