Barnes G-function

In mathematics, the Barnes G-function G(z) is a function that is an extension of superfactorials to the complex numbers. It is related to the gamma function, the K-function and the Glaisher–Kinkelin constant, and was named after mathematician Ernest William Barnes. It can be written in terms of the double gamma function. Formally, the Barnes G-function is defined in the following Weierstrass product form: where is the Euler–Mascheroni constant, exp(x) = ex, and ∏ is capital pi notation.

Barnes G-function

In mathematics, the Barnes G-function G(z) is a function that is an extension of superfactorials to the complex numbers. It is related to the gamma function, the K-function and the Glaisher–Kinkelin constant, and was named after mathematician Ernest William Barnes. It can be written in terms of the double gamma function. Formally, the Barnes G-function is defined in the following Weierstrass product form: where is the Euler–Mascheroni constant, exp(x) = ex, and ∏ is capital pi notation.